Question

When making a vertical jump, a grasshopper extends its legs 2.5 (cm) by 0.025 [s].
(a) What is your grasshopper acceleration while spreading its legs?
(b) What is the speed of the grasshopper when it leaves the ground, that is, at the moment in which
Are its legs fully extended?
(c) At what height does the grasshopper rise?

Answer 1

The distance travelled = 2.5 cm = 0.025m

time taken = 0.025s

using S=ut +0.5at2

where a = acceleration and u = initial velocity = 0 thus

a = 80 m/s2

using v2 = u2 + 2aS

since u =0, a = 80 and S = 0.025

v= 2m/s

since at the point the grasshopper stops accelerating with a = 80 , the velocity becomes 2 m/s

At highest point, the velocity becomes 0

and for this the acceleration is g = 9.8

thus using v2 = u2 + 2aS

where u = 2 , v= 0 and a = -9.8

thus S =20.4 cm

thus total height = 20.4 + 2.5 = 22.9 cm is the maximum height reached