Question

A toy jumps upward when you press a switch. Suppose it rises 0.54m in the first 0.2 seconds, how much higher does it go from the ground?

Answer 1

Given the vertical displcement of toy is y = 0.54 m

time t = 0.2 s

let the initial velocity be u = ?

the acceleration in vertical direction is a = - g = - 9.8 m/s^2 (acts in downward direction)

from the equation

s = (u*t) + (1/2 * a * t^2)

here we have

y = (u * t) - (1/2 * g * t^2)

0.54 = (u * 0.2) - (1/2 * 9.8 * (0.2)^2)

we get u = 3.68 m/s

With this initial velocity let the toy reaches a maximum height s = H then

final velocity v = 0 m/s.

From the equation

v^2 - u^2 = 2 * a * s

Here

v^2 - u^2 = 2 * (-g) * H

0^2 - (3.68)^2 = 2 * (-9.8) * H

H = 0.69 m

This the height for the toy from the ground