Positive (Upward) Launch Practice Problems

Plants depend on the explosive mechanism for seed dispersal. A pod opens up explosively on a level ground firing a seed with an initial velocity of 55 m/s at 54.0° above the horizontal. Assuming negligible air resistance, find the seed's horizontal and vertical components of acceleration and velocity at the highest point in its trajectory.

A pod lying on horizontal ground explosively fires a seed with an initial velocity of 33 m/s at 37° above the horizontal. Where does the seed land relative to the position of the pod assuming the seed feels negligible air resistance?

Seeds of Hum crepitans have launch velocities as high as 70 m/s. in the seed explosive mechanism of dispersal. A seed with this observed speed is fired from a  level ground at 22.3° above the horizontal. Assuming negligible air resistance, what is the maximum height reached above the ground?

A toy gun on a horizontal surface fires a bullet at 70° above the horizontal. If the bullet has an initial velocity of 39 m/s and feels negligible air resistance, after how long does the bullet reach the highest point in its trajectory?

A coin lying on a level ground is fired so that it acquires a velocity of 24 m/s directed at 38.0° above the horizontal. Determine the horizontal and vertical components of the coin's initial velocity if air resistance is negligible.  

The study of animal jumps is common in the academic discipline. The jumps are often reported in multiples of body length. Grasshoppers have attained maximum heights of 95.2 cm above the ground. If a grasshopper leaps at 54.0° above the horizontal, determine the takeoff speed for the leap.

An angry woman, after fighting with her boyfriend, tossed a pendant with an astonishing initial horizontal velocity component of 80 m/s and an initial vertical velocity component of 50 m/s. Calculate the distance that the pendant traveled after it was thrown. Ignore air resistance.

An orange was thrown with an initial upward velocity component of 50 m/s. The initial horizontal velocity component is half of this value. Calculate the time of flight of the orange. Treat the fruit as a point object (its weight is negligible) and ignore air resistance.

A softball was thrown with an initial horizontal velocity component of 15.0 m/s. The initial upward velocity component is equal to this value. After some time, the softball reaches the highest point of the trajectory. How high is this point? Ignore air resistance.

From sea level, an archer stands on the edge of a cliff that is 20 m above the ground. He fires an arrow with a speed of 70 m/s at an angle of 58° above the horizontal. Draw the x-t, y-t, u_x-t, and u_y-t graphs for the motion of the arrow upon shooting. Ignore air resistance.

On top of a building, a ball is thrown towards a taller building a certain distance away.  The initial velocity of the ball is 14.5 m/s at 21.5° above the horizontal. It hits the ground 3.8 s later. Ignore air resistance. What are the components of the ball's velocity initially and at the end of its trajectory?

In an arcade, you can get more arcade tickets the more balls you shoot through a ring in the game machine. The ring is placed above the point where you throw the ball, 1.5 m away from you (horizontally). If you throw the ball with a velocity of 30.0 m/s at an angle of 25°, the ball will pass through the ring. What is the vertical component of the velocity of the ball just before it passes through the ring? Ignore air resistance. 

You play a game with your friends, for which you are to throw a disc on the top of a rocky mound from a certain distance. During your turn, the disc is launched upward at an angle of 35° to the horizontal and lands on the top edge of a rocky mound that is 36 m away. The launching speed of the ball is 24.0 m/s. Ignoring air resistance, find the height of the rocky mound.

An athlete a few meters above the level ground throws a javelin with a velocity of 20.0 m/s, 46° above the horizontal. How far did she throw the javelin horizontally, if 4.11 s later, the javelin hits the ground? Ignore air resistance.

Astronauts are on a space mission to do research work. As a part of this mission, they throw a projectile on an unknown planet which follows the projectile path shown below. The projectile's status at an interval of 2 s is shown from 0 s to 6 s. The ball's velocity at t = 2 s is v = (3.0 i + 5.0 j). Calculate the velocity of the projectile at t = 0 s, 4 s, 6 s.

Imagine a real-life situation and develop a story for which the following kinematic equations will be satisfied. 

(i) s = 0 m + (30cos40° m/s)t₁ and (ii) 0 m = 0 m + (30sin40° m/s)t₁ - (1/2)(9.8 m/s²)(t₁)² 

During a football match, a goalkeeper kicks the football at an angle of 40° above the horizontal which lands in front of another player at a distance of 65 m after 3.3 s. Determine the highest distance that the ball reaches above the ground.

A person throws a ball with a mass of 2.0 kg and a velocity of 10 m/s at an angle of 36° above the horizontal. A headwind blows against the ball with a constant magnitude horizontally. By what percentage will the range of the ball be reduced if the magnitude of the headwind force increases from 2.0 N to 3.0 N?

A projectile was launched initially with a horizontal velocity component of 8.0 m/s and an upward velocity component of 16.0 m/s. How long does it take until this projectile reaches the highest point of the trajectory? Ignore air resistance.

Some boys are playing basketball. One boy shoots the ball towards the basket at a height of 'h' from the ground. The ball has a takeoff speed of 12 m/s and a launch angle of 50° above the horizontal. The ball passes through the basket after 3.0 s. Determine the largest vertical displacement experienced by the ball.

Steven stays in an apartment located on the second floor of the building. One day while leaving for his office in a hurry he mistakenly takes a pouch containing the house keys along with his wallet. He comes to know about this when he reaches his car parked in front of the building gate. He immediately calls his son who is on the balcony and throws the key pouch with a speed of 25 m/s at an angle of 75°. His son catches it perfectly after 3.0 s. Calculate the impact speed of the pouch. Consider the balcony is located at the height of 'h'.

A hockey player wants to score a goal by shooting the puck past the goalie into the net. The puck has a mass of 0.2 kg and is initially at rest on the ice. The player hits the puck with a stick, giving it an initial speed of 20 m/s. However, there is a headwind blowing in the opposite direction of the shot, with a constant force of 5 N acting on the puck horizontally. Determine the angle at which the puck should be launched to achieve maximum range.

Hint: use the following expression d/dθ(A•cosθ•sinθ - B•sin²θ) = A•cos(2θ) - B•sin(2θ)

An animation series designed for entertainment purposes for children comprises a scene that shows aliens playing catch. The figure given below shows the path followed by the ball and also the location of the ball. At the time t = 2 s, the ball has a velocity of (3.5i + 4.0j) m/s. Determine the value of acceleration due to gravity on the imaginary planet.

A skier glides down a slope inclined at $20^{\circ }$. Partway down the slope, the skier hits a small bump and takes off at an angle of $25^{\circ }$ above the horizontal. The skier then lands $2.5\ m$ further down the slope. Calculate the initial velocity of the skier at the moment of takeoff.

A soccer player kicks a ball from the ground, giving it a launch speed with a horizontal component of 15.0 m/s. If the ball is capable of traveling a horizontal distance of 45.0 m before touching the ground again, calculate the time the ball is in the air and the maximum height it reaches.

A skateboarder is performing tricks at a skatepark. During a trick, the skateboarder launches off a ramp at an angle θ₀ = 35° and achieves a horizontal range R = 3.0 m. What is the average horizontal velocity of the skateboarder as they perform the trick? 

A space explorer conducts tests on a remote asteroid, employing a tennis racket to strike a tennis ball. The ball traverses roughly 120 m across the asteroid's terrain. Given that the swing, launch angle, and other variables remain consistent, if the same explorer were to strike the ball on Earth, where it typically travels only 25 m, deduce the acceleration due to gravity on the asteroid's surface.

(Please note: Air resistance is insignificant on both the asteroid and Earth. Assume that the tennis ball takes off and lands at the same height).

A curious inventor constructs a toy rocket launcher and decides to calculate the maximum horizontal range of the toy rockets it launches. After setting it up, they launch a toy rocket vertically up, and it takes 4.5 s for the rocket to glide back down to the launcher. What is the maximum horizontal range of the toy rocket?

A ball is launched from the top of a tower that is 150 m tall as shown below. The ball is given an initial velocity of 45.0 m/s at an angle of 25.0° above the horizontal. Calculate the time it takes for the ball to reach the ground.

A stone is thrown from the edge of a bridge that is 100 m above a river. The stone is thrown with an initial velocity of 40.0 m/s at an angle of 40.0° with respect to the horizontal. Calculate the distance from the base of the bridge to the point where the stone hits the water. 

An egg drop project is launched from the top of a skyscraper that is 250 meters tall. The protective container holding the egg is given an initial velocity of 30.0 m/s at an angle of 50.0° with respect to the horizontal. Determine the horizontal and vertical components of the velocity of the protective container at the instant it hits the ground.

An athlete throws a javelin from ground level with an initial speed of 18.0 m/s. To achieve a horizontal distance of 30.0 meters, there are two possible angles of release. For each of these angles, find the maximum height the javelin reaches during its flight.

An archer shoots an arrow at a target that is level with the arrow at release. The arrow is shot at an angle of 30.0° above the horizontal and hits the target 70.0 m away. Calculate the initial speed of the arrow.

A water balloon is released from a stationary hot air balloon that is 100 meters above the ground as shown below. The water balloon is released with an initial velocity of 15.0 m/s at an angle of 30.0° from the horizontal. Calculate the magnitude of the velocity of the water balloon at the instant it lands.

A flare is launched from a stationary boat 15 meters above the water, with an initial velocity of 20.0 m/s at an angle of 60.0° with respect to the horizontal as shown. Calculate the angle made by the velocity vector with the horizontal as the flare lands in the water.

A stone is thrown from a bridge with an initial velocity of 12.0 m/s at an angle of 60.0° above the horizontal. The bridge is 30 meters above a river. Calculate the maximum height above the river reached by the stone.

A soccer player kicks a ball, launching it into the air at the moment the clock starts ticking (t=0) as shown. The ball has an initial velocity of 20 m/s, directed at an upward angle of 45° above ground. Meanwhile, a goalkeeper stands ready, positioned 50 m away from the point of the kick. From the perspective of the kick-off point, the goalkeeper's direct line of sight to the home spot forms a horizontal angle of 30° with the plane of the ball's flight path. Determine the speed and direction the goalkeeper must move in to intercept the ball at the same height from which it was initially kicked. Give the angle with respect to the goalkeeper's line of sight to the kickpoint. Hint: Use laws of sines and cosines

A parkour athlete jumps from the edge of one building to land on another building 1.5 s later, 3.5 m away horizontally to the right. The second building is 3.0 m lower than the first. Considering the athlete as a particle, find the athlete's initial velocity $\vec{v_0}$ , at the moment of the jump.

An archer aims to hit a target on a tower, with the center of the target being 18.0 m above the ground and 50.0 m away horizontally as shown. The archer releases the arrow from a height of 1.5 m. To ensure the arrow hits the target with a purely horizontal velocity component for a precision strike, what must be the horizontal speed of the arrow as it hits the target?