Some cats can be trained to jump from one location to another and perform other

Question

Some cats can be trained to jump from one location to another and perform other tricks. Kit the cat is going to jump through a hoop. He begins on a wicker cabinet at a height of 1.765 m above the floor and jumps through the center of a vertical hoop, reaching a peak height 3.120 m above the floor. (Assume the center of the hoop is at the peak height of the jump. Assume that +x axis is in the direction of the hoop from the cabinet and +y axis is up. Assume g = 9.81 m/s^2.) (a) With what initial velocity did Kit leave the cabinet if the hoop is at a horizontal distance of 1.560 m from the cabinet? v_0 = m/s (b) If Kit lands on a bed at a horizontal distance of 3.582 m from the cabinet, how high above the ground is the bed? m

Explanation / Answer

max height of cat's jump above launch height = 3.120 - 1.765 = 1.355 m

h = 1/2gt²

1.355 = 1/2gt²

t = ?[2(1.355)/9.81] = 0.526 s {time for cat to reach max height}

Voy = initial vertical component of cat's jump velocity = gt = 9.81(0.526) = 5.156 m/s

Vox = constant horizontal component of ca'ts velocity

= 1.56/t = 1.56/0.526 = 2.97 m/s

cat's initial velocity = 5.156i + 2.97j (ANS)

B)

time for cat to reach bed = 3.582/2.97 = 1.21 s

time for cat to Free-Fall from its max height to bed

T = 1.21 - 0.526 = 0.68 s

vertical distance fallen from max height in T

= 1/2gT² = 0.5(9.81)(0.68)² ? 2.27 m

height of bed off of ground = 3.120 - 2.27 = 0.85 m (Ans)

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