To determine the time it takes for the kangaroo to reach maximum height, we need to analyze the vertical component of its initial velocity. This can be calculated using the following formula:

$v_{y0} = v_0 \sin(\theta)$

Where:

• $v_0$ is the initial velocity (6.32 m/s),
• $\theta$ is the angle of projection (55.8 degrees),
• $v_{y0}$ is the vertical component of the initial velocity.

Once we have the vertical component, the time to reach maximum height can be found using the equation:

$t = \frac{v_{y0}}{g}$

Where $g$ is the acceleration due to gravity (approximately 9.81 m/s²).

Now let's calculate this.The time it takes for the kangaroo to reach maximum height is approximately 0.533 seconds.

Would you like any further explanation or details on this calculation?

Here are some related questions you might find interesting:

1. How high does the kangaroo jump?
2. What is the total time the kangaroo spends in the air?
3. What is the horizontal distance traveled by the kangaroo during the entire jump?
4. How does changing the angle of the jump affect the maximum height?
5. What would happen if the kangaroo jumps at a higher speed?

Tip: The vertical velocity becomes zero at the maximum height, which is why we use that point to calculate the time to reach the peak.