Name: _____________________________ Class: __________________Date: __________________

© Houghton Mifflin Harcourt Publishing Company Changes to the original content are the responsibility of the instructor.

Holt McDougal Physics i Sample Problem Set I

Sample Problem Set I Solutions

Two-Dimensional Motion and Vectors

ADDITIONAL PRACTICE E

Name: _____________________________ Class: __________________Date: __________________

© Houghton Mifflin Harcourt Publishing Company Changes to the original content are the responsibility of the instructor.

Holt McDougal Physics ii Sample Problem Set I

Name: _____________________________ Class: __________________Date: __________________

© Houghton Mifflin Harcourt Publishing Company Changes to the original content are the responsibility of the instructor.

Holt McDougal Physics 1 Sample Problem Set I

Two-Dimensional Motion and Vectors

Problem E PROJECTILES LAUNCHED AT AN ANGLE PROBLEM A zookeeper finds an escaped monkey on a pole. While aiming her tranquilizer gun at the monkey, she kneels 10.0 m from the pole, which is 5.00 m high. The tip of her gun is 1.00 m above the ground. At the moment the zookeeper shoots, the monkey drops a banana. The dart travels at 50.0 m/s. Will the dart hit the monkey, the banana, or neither one? SOLUTION 1. DEFINE Select a coordinate system. The positive y-axis points up, and the positive x-axis points along the ground toward the pole. Because the dart leaves the gun at a height of 1.00 m, the vertical distance is 4.00 m.

2. PLAN Use the inverse tangent function to find the angle of the dart with the x-axis.

θ = tan−1 Δy

Δx⎛

⎝⎜

⎞

⎠⎟= tan−1 4.00 m

10.0 m⎛

⎝⎜

⎞

⎠⎟= 21.8°

Choose a kinematic equation to solve for time. Rearrange the equation for motion along the x-axis to isolate Δt, the unknown, the time the dart takes to travel the horizontal distance.

Δx = (vi cosθ )Δt

Δt = Δxvi cosθ

=10.0 m

(50.0 m/s) (cos 21.8°)= 0.215 s

Find out how far each object will fall during this time. Use the free-fall kinematic equation. For the banana, vi = 0. Thus:

Δyb =

12

ay (Δt)2 =12

( −9.81m/s2 )(0.215 s)2 = −0.227 m

The dart has an initial vertical component of velocity of vi sin θ, so:

Δyd = (vi sinθ )Δt + 12

ay (Δt)2

Δyd = ( 50.0 m/s )(sin 21.8°)(0.215 s) + 12

( −9.81 m/s2 )(0.215 s)2

Δyd = 3.99 m − 0.227 m = 3.76 m

Name: _____________________________ Class: __________________Date: __________________

© Houghton Mifflin Harcourt Publishing Company Changes to the original content are the responsibility of the instructor.

Holt McDougal Physics 2 Sample Problem Set I

Find the final height of both the banana and the dart.

yb, f = yb,i +Δyb = 5.00 m + (−0.227 m) =

4.77 m above the ground

yd , f = yd ,i +Δyd =1.00 m + 3.76 m =

4.76 m above the ground

The dart hits the banana. The slight difference is due to rounding.

ADDITIONAL PRACTICE 1. In 1993, Wayne Brian threw a spear a record distance of 201.24 m. (This is not an official

sport record because a special device was used to “elongate” Brian’s hand.) Suppose Brian threw the spear at a 35.0° angle with respect to the horizontal. What was the initial speed of the spear?

2. April Moon set a record in flight shooting (a variety of long-distance archery). In 1981 in Utah, she sent an arrow a horizontal distance of 9.50 × 102 m. What was the speed of the arrow at the top of the flight if the arrow was launched at an angle of 45.0° with respect to the horizontal?

3. In 1989 during overtime in a high school basketball game in Erie, Pennsylvania, Chris Eddy threw a basketball a distance of 27.5 m to score and win the game. If the shot was made at a 50.0° angle above the horizontal, what was the initial speed of the ball?

4. In 1978, Geoff Capes of the United Kingdom won a competition for throwing 5 lb bricks; he threw one brick a distance of 44.0 m. Suppose the brick left Capes’ hand at an angle of 45.0° with respect to the horizontal.

a. What was the initial speed of the brick?

b. What was the maximum height reached by the brick?

c. If Capes threw the brick straight up with the speed found in (a), what would be the maximum height the brick could achieve?

5. In 1991, Doug Danger rode a motorcycle to jump a horizontal distance of 76.5 m. Find the maximum height of the jump if his angle with respect to the ground at the beginning of the jump was 12.0°.

6. Michael Hout of Ohio can run 110.0 meter hurdles in 18.9 s at an average speed of 5.82 m/s. What makes this interesting is that he juggles three balls as he runs the distance. Suppose Hout throws a ball up and forward at twice his running speed and just catches it at the same level. At what angle, θ, must the ball be thrown? (Hint: Consider horizontal displacements for Hout and the ball.)

Name: _____________________________ Class: __________________Date: __________________

© Houghton Mifflin Harcourt Publishing Company Changes to the original content are the responsibility of the instructor.

Holt McDougal Physics 3 Sample Problem Set I

7. A golfer hits a golf ball at an angle of 25.0° to the ground. If the golf ball covers a

horizontal distance of 301.5 m, what is the ball’s maximum height? (Hint: At the top of its flight, the ball’s vertical velocity component will be zero.)

8. In a scene in an action movie, a stuntman jumps from the top of one building to the top of another building 4.0 m away. After a running start, he leaps at a velocity of 5.0 m/s at an angle of 15° with respect to the flat roof. Will he make it to the other roof, which is 2.5 m lower than the building he jumps from?