A kangaroo can jump over an object 2.50 m high.(a) Calculate its vertical speed when it leaves the ground.(b) Calculate how long is it in the air

Sure, let's solve this problem step by step.

(a) To calculate the vertical speed of the kangaroo when it leaves the ground, we can use the following equation from physics:

v² = u² + 2gs

where: v is the final velocity (which is 0 in this case because the kangaroo reaches a height where its velocity is 0), u is the initial velocity (which we are trying to find), g is the acceleration due to gravity (approximately 9.8 m/s²), and s is the distance (the height the kangaroo jumps, which is 2.5 m).

Rearranging the equation to solve for u gives us:

u = sqrt(v² - 2gs)

Substituting the given values into the equation gives us:

u = sqrt(0 - 2*(-9.8)*2.5) = sqrt(49) = 7 m/s

So, the kangaroo's vertical speed when it leaves the ground is 7 m/s.

(b) To calculate how long the kangaroo is in the air, we can use the following equation from physics:

t = (v - u) / g

where: t is the time (which we are trying to find), v is the final velocity (which is 0 in this case because the kangaroo reaches a height where its velocity is 0), u is the initial velocity (which we found to be 7 m/s in part (a)), and g is the acceleration due to gravity (approximately 9.8 m/s²).

Substituting the given values into the equation gives us:

t = (0 - 7) / -9.8 = 0.714 s

So, the kangaroo is in the air for approximately 0.714 seconds.