My cat can jump straight up and reach a fence 1.5 m high. Find her initial veloc

Question

My cat can jump straight up and reach a fence 1.5 m high. Find her initial velocity assuming free-fall. Later on I saw my cat jump from the deck (H_0 = 0.5 m) in my backyard to a bird feeder (H_1 = 1.7m) on a tree from the deck. Assume the cat has the same initial velocity as in part (a) above (if you didn't get a velocity, make a reasonable one), If the cat reaches the bird feeder at highest point in her jump, find the angle from horizontal that she must jump to catch the bird. Find her acceleration and velocity (vectors) when she reaches the bird feeder. The cat missed the bird feeder and hit the tree at the same height she left the deck. Find the speed (magnitude) that she had just before she hit the tree!

Explanation / Answer

by conservation of energy

initial energy = final energy

mgh = 0.5 * mv^2

gh = 0.5 * v^2

9.8 * 1.5 = 0.5 * v^2

v = 5.42 m/s

initial velocity of cat = 5.42 m/s

after jumping from the fence the cat is following the projectile motion

maximum height = v^2 * sin^2(theta) / 2g

(1.7 - 0.5) = 5.42 * sin^2(theta) / (2 * 9.8)

theta = 40.96 degree

cat must jump at 40.96 degree

velocity at the heighest point = -v * cos(40.96)i

velocity at heighest point = -5.42 * cos(40.96)i

velocity at heighest point = -4.09i m/s

acceleration at the heighest point = 0 m/s^2

speed when cat hits the tree = 5.42 m/s

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