Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

$$\frac{v_0$^2 \sin^2$\theta}{2g}$$

Question 1

A particle's velocity as a function of time is given by $$v(t) = (2.3\ \mathrm{m/s}) + (4.1\ \mathrm{m/s^2$})t - (6.2\ \mathrm{m/s^3$})t^2$. What is the average acceleration of the particle between t = 1.0$$\ \mathrm{s}$$ and t = 2.0$$\ \mathrm{s}$$?

Accepted Answer

$$-13\ \mathrm{m/s^2$}$$

Question 2

A jet plane is launched from a catapult on an aircraft carrier. In $$2.0\ \mathrm{s} it $$reaches a speed of $$42\ \mathrm{m/s} at $$the end of the catapult. Assuming the acceleration is constant, how far did it travel during those $$2.0\ \mathrm{s}$$?

Accepted Answer

$$24\ \mathrm{m}$$

Question 3

An object starts from rest and undergoes uniform acceleration. During the first second it travels $$5.0\ \mathrm{m}. $$How far will it travel during the third second?

Accepted Answer

$$25\ \mathrm{m}$$

Question 4

A toy rocket is launched vertically from ground level at time $$t = 0.00\ \mathrm{s}. $$The rocket engine provides constant upward acceleration during the burn phase. At the instant of engine burnout, the rocket has risen to $$81\ \mathrm{m}$$ and acquired an upward velocity of $$40\ \mathrm{m/s}. $$The upward acceleration of the rocket during the burn phase is closest to

Accepted Answer

$$9.6\ \mathrm{m/s^2$}$$

Question 5

A rock is projected upward from the surface of the Moon, at time $$t = 0\ \mathrm{s}$$, with an upward velocity of $$30.0\ \mathrm{m/s}. $$The acceleration due to gravity at the surface of the Moon is $$1.62\ \mathrm{m/s^2$}$$, and the Moon has no atmosphere. The height of the rock when it is descending with a speed of $$20.0\ \mathrm{m/s} is $$closest to

Accepted Answer

$$154\ \mathrm{m}$$

Question 6

To determine the height of a bridge above the water, a person drops a stone and measures the time it takes for it to hit the water. If the time is $$2.3\ \mathrm{s}$$, what is the height of the bridge? Neglect air resistance.

Accepted Answer

$$32\ \mathrm{m}$$

Question 7

A ball is thrown at an original speed of $$8.0\ \mathrm{m/s} at an $$angle of $$35^\circ$$ above the horizontal. If there is no air resistance, what is the speed of the ball when it returns to the same horizontal level?

Accepted Answer

$$8.0\ \mathrm{m/s}$$

Question 8

A girl throws a rock horizontally, with a velocity of $$10\ \mathrm{m/s}$$, from a bridge. It falls $$20\ \mathrm{m} to $$the water below. How far does the rock travel horizontally before striking the water, assuming negligible air resistance?

Accepted Answer

$$16\ \mathrm{m}$$

Question 9

A cat leaps to try to catch a bird. If the cat's jump was at $$60^\circ$$ off the ground and its initial velocity was $$2.74\ \mathrm{m/s}$$, what is the highest point of its trajectory, neglecting air resistance?

Accepted Answer

$$0.29\ \mathrm{m}$$

Question 10

As shown in the figure, a projectile is fired at time $$t = 0.00\ \mathrm{s}$$, from point $$O at $$the upper edge of a cliff, with initial velocity components of $$v_{0x} = 30\ \mathrm{m/s}$$ and $$v_{0y} = 300\ \mathrm{m/s}. $$The projectile rises and then falls into the sea at point $$P. $$The time of flight of the projectile is $$75.0\ \mathrm{s}$$, and air resistance is negligible. At this location, $$g = 9.80\ \mathrm{m/s^2$}. $$What is the horizontal distance $$D$$?

Accepted Answer

$$2790\ \mathrm{m}$$

Question 11

A hobbyist launches a projectile from ground level on a horizontal plain. It reaches a maximum height of $$72.3\ \mathrm{m}$$ and lands $$111\ \mathrm{m}$$ from the launch point, with no appreciable air resistance. What was the angle of launch if $$g = 9.80\ \mathrm{m/s^2$}$$?

Accepted Answer

$$44.8^\circ$$

Question 12

A projectile is fired from ground level on a horizontal plain. If the initial speed of the projectile is now doubled, and we neglect air resistance, what happens to its range?

Accepted Answer

Its range will quadruple.

Question 13

A car accelerates uniformly from rest to a speed $$v in $$time $$t. $$What is the distance traveled by the car in this time?

Accepted Answer

$$\frac{1}{2}vt$$

Question 14

A ball is thrown straight up with an initial velocity $$v_0. $$Neglecting air resistance, what is the total time the ball spends in the air before returning to the thrower's hand?

Accepted Answer

$$\frac{2v_0}{g}$$

Question 15

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

Accepted Answer

$$\frac{v_0$^2 \sin^2$	heta}{2g}$$

Question 16

A stone is thrown horizontally from the top of a cliff with speed $$v_0. If $$the cliff is $$h$$ meters high, how long does it take for the stone to reach the ground?

Accepted Answer

$$\sqrt{\frac{2h}{g}}$$

Question 17

A projectile is launched with initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the time of flight until it returns to the same vertical level?

Accepted Answer

$$\frac{2v_0 \sin	heta}{g}$$

Physics with Calculus: Kinematics and Projectile Motion Practice

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