Question 1

A soccer ball is released from rest at the top of a grassy incline and travels 87 m in 8.6 s. Assuming constant acceleration, what is the magnitude of the ball's acceleration? Use $$d = v_0$ t + \frac{1}{2} a t^2$.

Accepted Answer

$$a = 2.4\ \mathrm{m/s^2$}$$

Question 2

A package is dropped from a helicopter moving upward. If it takes $$14.3\ \mathrm{s} to $$hit the ground and air resistance is negligible, what was the height from which it was dropped? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ and $$v_0 = 0$ for the vertical motion.)

Accepted Answer

$$h = 1000\ \mathrm{m}$$

Question 3

A ball is projected upward from a roof $$90\ \mathrm{m}$$ above the ground. If the initial velocity is $$15\ \mathrm{m/s}$$ upward, and air resistance is negligible, what is the time when the ball strikes the ground? (Use $$y = y_0$ + v_0$ t - \frac{1}{2} g t^2$.)

Accepted Answer

$$t = 9.4\ \mathrm{s}$$

Question 4

A rock is dropped from a cliff and takes $$3.00\ \mathrm{s} to $$reach the ground. A second rock is thrown downward and takes $$2.00\ \mathrm{s} to $$reach the ground. What was the initial velocity of the second rock? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$12.3\ \mathrm{m/s}$$ downward

Question 5

A foul ball is hit straight up with a speed of $$30.0\ \mathrm{m/s}. $$How long does it take to reach its maximum height? (Use $$v = v_0$ - g t.)$$

Accepted Answer

$$3.06\ \mathrm{s}$$

Question 6

A foul ball is hit straight up with a speed of $$30.0\ \mathrm{m/s}. $$What is the maximum height reached by the ball? (Use $$h = \frac{v_0$^2}{2g}.)$$

Accepted Answer

$$45.9\ \mathrm{m}$$

Question 7

A foul ball passes a point $$25.0\ \mathrm{m}$$ above the bat at two different times. Why are there two answers for the time at which this occurs?

Accepted Answer

The ball passes the point once going up and once coming down.

Question 8

A test rocket is fired straight up from rest with a net acceleration of $$20.0\ \mathrm{m/s^2$}$$ for $$4.00\ \mathrm{s}. $$After the motor turns off, the rocket coasts upward. What is the maximum elevation reached by the rocket? (Neglect air resistance.)

Accepted Answer

$$487\ \mathrm{m}$$

Question 9

A ball is launched vertically from $$20\ \mathrm{m}$$ above the ground at the same time a car $$30\ \mathrm{m}$$ away moves toward the launch point with $$v_0 = 5.0$$\ \mathrm{m/s}$$ and a = 3.0$$\ \mathrm{$$m/s^2$$}$$. If the ball lands on the car, what is the initial velocity of the ball? (Assume g = 9.8$$\ \mathrm{$$m/s^2$$}$$.)

Accepted Answer

$$14.0\ \mathrm{m/s}$$

Question 10

A soccer ball rolls down an incline, traveling $$87\ \mathrm{m} in$$ $$8.6\ \mathrm{s}$$ and then $$23\ \mathrm{m} in $$the next $$1.0\ \mathrm{s}. $$What is the total length of the incline?

Accepted Answer

$$110\ \mathrm{m}$$

Question 11

A ball is thrown vertically upward from a roof $$90\ \mathrm{m}$$ above the ground with an initial velocity of $$15\ \mathrm{m/s}. $$How long does it take to reach its maximum height? (Use $$v = v_0$ - g t.)$$

Accepted Answer

$$1.53\ \mathrm{s}$$

Question 12

A rock is dropped from a cliff and takes $$3.00\ \mathrm{s} to $$reach the ground. What is the height of the cliff? (Use $$h = \frac{1}{2} g t^2$.)

Accepted Answer

$$44.1\ \mathrm{m}$$

Question 13

A test rocket accelerates upward at $$20.0\ \mathrm{m/s^2$}$$ for $$4.00\ \mathrm{s}$$, then coasts upward. What is the rocket's velocity when the motor turns off?

Accepted Answer

$$80.0\ \mathrm{m/s}$$

Question 14

A ball is hit straight up with $$30.0\ \mathrm{m/s}. At $$what time does it pass $$25.0\ \mathrm{m}$$ above the bat on the way up? (Use $$y = v_0$ t - \frac{1}{2} g t^2$.)

Accepted Answer

$$0.995\ \mathrm{s}$$

Question 15

A ball is hit straight up with $$30.0\ \mathrm{m/s}. At $$what time does it pass $$25.0\ \mathrm{m}$$ above the bat on the way down?

Accepted Answer

$$5.13\ \mathrm{s}$$

Question 16

A car starts $$30\ \mathrm{m}$$ from a point and moves toward it with $$v_0 = 5.0$$\ \mathrm{m/s}$$ and a = 3.0$$\ \mathrm{$$m/s^2$$}$$. How long does it take to reach the point? (Use x$$ = $$x_0$$ + $$v_0 t$$ + \frac{1}{2} a $$t^2.)$$

Accepted Answer

$$2.0\ \mathrm{s}$$

Question 17

A package is dropped from a helicopter. If it takes $$14.3\ \mathrm{s} to $$hit the ground, what is its average velocity during the fall?

Accepted Answer

$$70.0\ \mathrm{m/s}$$

Question 18

A soccer ball is released from rest and travels $$87\ \mathrm{m} in$$ $$8.6\ \mathrm{s}. $$What is its final velocity at the end of $$8.6\ \mathrm{s}$$? (Use $$v = v_0$ + a t.)$$

Accepted Answer

$$20.6\ \mathrm{m/s}$$

Step-by-Step Physics Guidance: Kinematics and Projectile Motion

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