A grasshopper jumps at a 65.0 degree angle at 5.42m/s. At what time does it reach its maximum height?

When the grasshoppers vertical velocity is exactly zero.
v = -g•t + v0.
v: vertical part of velocity. Is zero at maximum height.
g: 9.81
t: time you are looking for
v0: initial vertical velocity
Find the vertical part of the initial velocity, by using the angle at which the grasshopper jumps.

Answer Link

CarliReifsteck CarliReifsteck · Answer 2 · 2019-09-18T02:10:02-04:00

Answer:

A grasshopper reached the maximum height 1.23 m.

Explanation:

Given that,

Velocity = 5.42 m/s

Angle = 65.0°

We need to calculate the maximum height

Using formula of maximum height

\(y_{max}=\dfrac{v^2\sin^2\theta}{2g}\)

Where, v = 5.42 m/s

g = acceleration due to gravity

\(\theta\) =Angle

Put the value into the formula

\(y_{max}=\dfrac{5.42^2\times\sin^2(65.0)}{2\times9.8}\)

\(y_{max}=1.23\ m\)

Hence, A grasshopper reached the maximum height 1.23 m.