NAME_______ ANSWERS BOOK WORK CHAPTER 3 Projectiles

Pg. 102

1) A pelican flying along a horizontal path drops a fish from a height of 5.4 m while traveling 5 m/s. How far does the fish travel horizontally before it hits the water below?

__X__

Vx = 5 m/s

Dx =??

T=??

Dx=Vx T

__Y__

Viy = 0 m/s

Ay = -9.8 m/s^{2}

Dy= -5.4 m

Dy = Viy T + ½ Ay T^{2}

-5.4 = 0 (T) + ½ (-9.8) T^{2}

-5.4 = -4.9 T^{2}

T= 1.05 sec

Back to X

Dx=5(1.05)=5.25 m

2) Give both the horizontal and vertical components of the velocity of the fish from item 1 before the fish enters the water. ( Find Vfx and Vfy if Dy= -5.4m, Vix= 5 m/s , Viy=0 )

__X__

Vfx=Vx= 5 m/s

__Y__

Dy = -5.4 m

Ay = -9.8 m/s^{2}

Viy = 0 m/s

Vfy = ????

Vfy^{2}=Viy^{2} + 2 Ay Dy

Vfy^{2}=(0) + 2 (-9.8) ( -5.4)

Vfy^{2}=105.84

Vfy = - 10.29 m/s (downward)

For the final velocity

**V**^{2} = Vx^{2}+
Vy^{2}

**V ^{2} = **5

**V= **11.44 m/s θ = tan ^{-1} ( Vy/Vx) =

tan ^{-1} (10.29/5) = 64 degrees to the water

Final Velocity is 11.44 m/s at 64 degrees to the water

3) Find the instantaneous velocity of the stunt dummy in Sample Problem 3D as it hits the water. ( Find Vfx and Vfy if Dy= - 10 m, Vix= 22.5 m/s , Viy=0 )

__X__

Vfx=Vx= 22.5 m/s

__Y__

Dy = -10 m

Ay = -9.8 m/s^{2}

Viy = 0 m/s

Vfy = ????

Vfy^{2}=Viy^{2} + 2 Ay Dy

Vfy^{2}=(0) + 2 (-9.8) ( -10)

Vfy^{2}=196

Vfy = - 14 m/s (downward)

For the final velocity

**V**^{2} = Vx^{2}+
Vy^{2}

**V ^{2} = **22.5

**V= **26.5m/s

θ = tan ^{-1} ( Vy/Vx) = tan ^{-1}
(14/22.55) = 31.9 degrees to the ground

Final Velocity is 25.5 m/s at 31.9 degrees to the ground

4) A cat chases a mouse across a 1.0 m high table. The mouse steps out of the way and the cat slides off the table at a speed of 5 m/s. Where does the cat strike the floor?

__X__

Vx = 5 m/s

Dx =??

T=??

Dx=Vx T

__Y__

Viy = 0 m/s

Ay = -9.8 m/s^{2}

Dy= -1 m

Dy = Viy T + ½ Ay T^{2}

-1 = 0 (T) + ½ (-9.8) T^{2}

-1 = -4.9 T^{2}

T= .45 sec

Back to X

Dx=5(.45)=2.26 m

ANSWERS Bookwork Chapter 3 pg. 105 Section Review (do on fresh paper so you have room!)

1) Which of the following are examples of projectile motion?

a) airplane taking off, ** b) tennis ball lobbed over a
net.** c) plastic disk
sailing over the lawn d) a hawk diving to catch a mouse e) a parachutist
drifting to Earth

2) Which of the following exhibit parabolic motion?

*a) a flat rock skipping over the surface of the lake*** b) a three point
shot in basketball**
c) the space shuttle while orbiting the Earth

3) An Alaskan rescue plane drops a package of emergency rations to s stranded party of explorers. The plane is traveling horizontally at 100 m/s at a height of 50 m above the ground. What horizontal distance does the package travel before striking the ground?

__X__

Vx = 100 m/s

Dx =??

T=??

Dx=Vx T

__Y__

Viy = 0 m/s

Ay = -9.8 m/s^{2}

Dy= -50 m

Dy = Viy T + ½ Ay T^{2}

-50 = 0 (T) + ½ (-9.8) T^{2}

-50 = -4.9 T^{2}

T= 3.19 sec

Back to X

Dx=100 (3.19)=319 m

4) Find the velocity (vector magnitude and direction) of the package in item 3 just before it hits the ground.

__X__

Vfx=Vx= 100 m/s

__Y__

Dy = -50 m

Ay = -9.8 m/s^{2}

Viy = 0 m/s

Vfy = ????

Vfy^{2}=Viy^{2} + 2 Ay Dy

Vfy^{2}=(0) + 2 (-9.8) ( -50)

Vfy^{2}= 980

Vfy = - 31.3 m/s (downward)

For the final velocity

**V**^{2} = Vx^{2}+
Vy^{2}

**V ^{2} = **100

**V= **104.7 m/s

θ = tan ^{-1} ( Vy/Vx) = tan ^{-1}
(31.3/100) = 31.9 degrees to the ground

Final Velocity is 104.7 m/s at 17.38 degrees to the ground

5) During a thunderstorm, a tornado lifts a car to a height of 125 m above the ground. Increasing in strength, the tornado flings the car horizontally with an initial speed of 90 m/s. How long does the car take to reach the ground? How far horizontally does the car travel before hitting the ground?

__X__

Vx = 90 m/s

Dx =??

T=??

Dx=Vx T

__Y__

Viy = 0 m/s

Ay = -9.8 m/s^{2}

Dy= -125 m

Dy = Viy T + ½ Ay T^{2}

-125 = 0 (T) + ½ (-9.8) T^{2}

-125 = -4.9 T^{2}

T= 5.05 sec

Back to X

Dx=90 ( 5.05)=454.57 m

*** 6) Streams of water in a fountain shoot from one level to the next. A particle of water in a stream takes 0.5 seconds to travel between the first and the second level. The receptacle on the second level is a horizontal distance of 1.5 m away from the spout on the first level. If the water is projected at a 33 ° angle, what is the initial speed of the particle?

__X__

Dx = 1.5 m

T = 0.5 sec

Dx = Vx T

1.5 = Vx (.5)

Vx = 3 m/s

Vx = V cos (θ)

3 = **V ** cos (33)

3 = **V **(.83867)

**V = ** 3.577 m/s

*** 7) If a water particle in a stream of water in a fountain takes 0.35 seconds to travel from spout to receptacle when shot at an angle of 67° and an initial speed of 5 m/s, what is the vertical distance between the levels of the fountain?

__Y__

Vy = **V** sin (θ)

Vy = 5 sin (67)

Viy = 4.6 m/s

Ay = - 9.8 m/s^{2}

T = 0.35 sec

Dy = ????

Dy = Viy T + ½ Ay T^{2}

Dy = 4.6 (.35)
+ ½ (-9.8) (.35)^{2}

Dy = 1.61 + -4.9 *.1225

Dy = 1.00975 m