5. Projectile Motion

Projectile Motion Problem

05:20

Jennifer Cash

227

Practice this topic

You throw a rock off the top of a tall building at an upward angle of 15°. At t=3 s, the rock's horizontal displacement from you is 52m. How high does the rock get above the top of the building?

532

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A ball is thrown from the top of a 50-m-tall building with a speed of 40 m/s at an angle of 37° above the horizontal. How far horizontally does the ball travel before hitting the ground?

Three footballs are punted into the air at

32 m / s

. Ball A has a launch angle of 34°, Ball B has a launch angle of 41°, Ball C has a launch angle of 57°. Which ball has the longest hang time? In other words, which ball is in the air for the longest time?

163

A baseball player hits a pop fly ball. If the ball leaves the bat at

45 m / s

at an angle of 68° above the horizontal, what is the maximum height, above the point of contact with the bat, that the ball will reach? Ignore air resistance.

287

A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0° above the horizontal. Ignore air resistance. Calculate (d) Draw x-t, y-t, υx–t, and υy–t graphs for the motion.

664

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (e) At its highest point, find the horizontal and vertical components of its acceleration and velocity.

1550

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On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (d) How far from its firing point does the shell land?

369

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (c) Find its maximum height above the ground.

250

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (b) How long does it take the shell to reach its highest point?

458

On level ground a shell is fired with an initial velocity of 40.0 m/s at 60.0° above the horizontal and feels no appreciable air resistance. (a) Find the horizontal and vertical components of the shell's initial velocity.

1068

The froghopper, Philaenus spumarius, holds the world record for insect jumps. When leaping at an angle of 58.0° above the horizontal, some of the tiny critters have reached a maximum height of 58.7 cm above the level ground. (See Nature, Vol. 424, July 31, 2003, p. 509.) (a) What was the takeoff speed for such a leap?

3039

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A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (d) How far has the football traveled horizontally during this time?

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A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (c) How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)?

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A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (b) How high is this point?

1383

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (b) What is the vertical component of the velocity of the quarter just before it lands in the dish?

2361

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In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. (a) What is the height of the shelf above the point where the quarter leaves your hand?

278

A shot putter releases the shot some distance above the level ground with a velocity of 12.0 m/s, 51.0° above the horizontal. The shot hits the ground 2.08 s later. Ignore air resistance. (c) How far did she throw the shot horizontally?

527

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A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. (a) How much time is required for the football to reach the highest point of the trajectory?

(II) You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 3.4 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

Apollo astronauts took a 'nine iron' to the Moon and hit a golf ball about 180 m. Assuming that the swing, launch angle, and so on, were the same as on Earth where the same astronaut could hit it only 32 m, estimate the acceleration due to gravity on the surface of the Moon. (We neglect air resistance in both cases, but on the Moon there is none.)

A ball is thrown toward a cliff of height h with a speed of 30 m/s and an angle of 60° above horizontal. It lands on the edge of the cliff 4.0 s later. c. What is the ball's impact speed?

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A ball is thrown toward a cliff of height h with a speed of 30 m/s and an angle of 60° above horizontal. It lands on the edge of the cliff 4.0 s later. b. What was the maximum height of the ball?

367

A physics student on Planet Exidor throws a ball, and it follows the parabolic trajectory shown in FIGURE EX4.13. The ball's position is shown at 1 s intervals until t = 3s. At t = 1s, the ball's velocity is v = (2.0 i + 2.0 j) m/s. (b) What is the value of g on Planet Exidor?

183

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In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched with speed into a headwind that exerts a constant, horizontal retarding force Fwᵢₙd = -Fwᵢₙd î. a. Find an expression for the angle at which the range is maximum.

204

In the absence of air resistance, a projectile that lands at the elevation from which it was launched achieves maximum range when launched at a 45° angle. Suppose a projectile of mass m is launched with speed into a headwind that exerts a constant, horizontal retarding force Fwᵢₙd = -Fwᵢₙd î. b. By what percentage is the maximum range of a 0.50 kg ball reduced if Fwᵢₙd = 0.60 N?

106

A child runs down a 12° hill and then suddenly jumps upward at a 15° angle above horizontal and lands 1.3 m down the hill as measured along the hill. What was the child's initial speed at the jump?

(II) An Olympic long jumper is capable of jumping 8.0 m. Assuming his horizontal speed is 9.1 m/s as he leaves the ground, how long is he in the air and how high does he go? Assume that he lands standing upright—that is, the same way he left the ground.

A grasshopper hops along a level road. On each hop, the grasshopper launches itself at angle θ₀ = 45 ° and achieves a range R = 0.80 m . What is the average horizontal speed of the grasshopper as it hops along the road? Assume that the time spent on the ground between hops is negligible.

(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45.

(a) Determine the time taken by the projectile to hit point P at ground level.

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(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45.

(b) Determine the distance X of point P from the base of the vertical cliff. At the instant just before the projectile hits point P.

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(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45. At the instant just before the projectile hits point P, find

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(II) If a ball is kicked from ground level at 15.0 m/s, there are two launch angles that will make the ball land 20.0 m away.

(b) What maximum height does the ball reach in each case?

(II) An athlete performing a long jump leaves the ground at a 27.0° angle and lands 7.80 m away.

(a) What was the takeoff speed?

(II) A projectile is shot from the edge of a cliff 125 m above ground level with an initial speed of 62.0 m/s at an angle of 35.0° with the horizontal, as shown in Fig. 3–45.. At the instant just before the projectile hits point P, find

(d) the magnitude of the velocity,

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(e) the angle made by the velocity vector with the horizontal.

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(f) Find the maximum height above the cliff top reached by the projectile.

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At t = 0 a batter hits a baseball with an initial speed of 28 m/s at a 55° angle to the horizontal. An outfielder is 85 m from the batter at t = 0 and, as seen from home plate, the line of sight to the outfielder makes a horizontal angle of 22° with the plane in which the ball moves (see Fig. 3–66). What speed and direction must the fielder take to catch the ball at the same height from which it was struck? Give the angle with respect to the outfielder's line of sight to home plate.

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A diver leaves the end of a 3.5-m-high diving board and strikes the water 1.3 s later, 3.0 m beyond the end of the board. Considering the diver as a particle, determine:

(a) her initial velocity, v₀ (→ above v);

(II) Romeo is throwing pebbles gently up to Juliet's window, and he wants the pebbles to hit the window with only a horizontal component of velocity. He is standing at the edge of a rose garden 8.0 m below her window and 8.5 m from the base of the wall (Fig. 3–48). How fast are the pebbles going when they hit her window?

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