1) The best leaper in the animal kingdom is the puma, which can jump to a height

Question

1) The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of 45°. With what speed must the animal leave the ground to reach that height?

_________________m/s

2) An artillery shell is fired with an initial velocity of 300 m/s at 57.0° above the horizontal. To clear an avalanche, it explodes on a mountainside 45.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?

x = _________ m

y = _________ m

Explanation / Answer

1)

along vertical

initial velocity voy = v*sintheta

acceleration ay = -g = -9.8 m/s^2

maximum height reached y = h = 3.7 m

at maximum height vinal velocity vy = 0

from equation of motion

vy^2 - voy^2 = 2*ay*y

0 - (v*sin45)^2 = -2*9.8*3.7

speed v = 12 m/s <<<<------------ANSWER

================

2)

along horizontal

initial velocity vox = v*costheta

acceleration ax = 0

time t = 45 s

position x = vox*t + (1/2)*ax*t^2

x = 300*cos57*45 + 0

x = 7352.6 m

along vertical

initial velocity voy = vo*sintheta

acceleration ay = -g = -9.8 m/s^2

displacement y = voy*t + (1/2)*ay*t^2

y = 300*sin57*45 - (1/2)*9.8*45^2

y = 1400 m

x = 7352.6 m

y = 1400 m

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