Question

A kangaroo can jump over an object 2.50 m high. (a) Considering just its vertical motion, calculate its vertical speed when it leaves the ground. (b) How long a time is it in the air?

a) 7.85 m/s
b) 0.50 s
c) 5.00 s
d) 1.26 m/s

Answer 1

The kangaroo's vertical speed when it leaves the ground is around 7.0 m/s, and it will be in the air for approximately 1.43 seconds when jumping over an object 2.50 m high.

Step-by-step explanation:

To determine the vertical speed of a kangaroo when it leaves the ground to jump over an object 2.50 m high, we can use the principles of kinematics for projectile motion under the influence of gravity. Assuming upward direction is positive and using the acceleration due to gravity g = -9.8 m/s2, the maximum height h reached by an object projected vertically with an initial velocity v0 is given by h = v02/(2g).

(a) To find its vertical speed when it leaves the ground, we rearrange the equation to solve for v0: v0 = √(2gh), which gives us v0 = √(2(-9.8 m/s2)(2.50 m)), resulting in v0 = 7.0 m/s.

(b) The total time in the air for a projectile can be found by doubling the time it takes to reach the maximum height since the ascent and descent durations are equal. Therefore, t = 2v0/g = 2(7.0 m/s)/(9.8 m/s2) gives us t ≈ 1.43 s as the total time the kangaroo is in the air.