11. A boy is at the top of a tree, 15.0 meters above the ground. There is a rabb

Question

11. A boy is at the top of a tree, 15.0 meters above the ground. There is a rabbit sitting o the ground, 30.0 meters from the base of the tree. The boy wants to hit the rabbit with a snowball, but because he doesn't know physics yet, he throws the snowball directly at t rabbit, such that the initial velocity vector of the snowball points directly at the rabbit, at an angle of 26.6 degrees below horizontal. Because the boy did not account for the acceleration due to gravity, the snowball flies through the air for 1.20 seconds before landing somewhere between the tree and the rabbit. 15.0 m 0 30.0 m a) how far from the base of the tree does the snowball land? b) what is the velocity of the snowball just before it hits the ground?

Explanation / Answer

H = 15 m

time of flight = 1.2 sec

let the velocity = u m/s

so the component of velocity

ux = u cos26.6 m/s

uy = u sin26.6 m/s

# now in Y - direction ( let downward directon as +)

H = uy T + 1/2 aT2

15 = ( u sin26.6 ) x 1.2 + 1/2 x 9.81 x 1.22

u = 15.m/s

A) Range = R = ux T = ( 15 cos26.6) x 1.2 = 16.1 m

B) let the velocity vefor hitting ground = v

from energy conservation b/w initial and final position

KEi+ PEi = KEf + PEf

1/2 m u2 + mgH = 1/2 m v2 + 0

1/2 (15)2 + 9.81 x 15 = v2/2

v = 22.78 m/s

answer

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