A squirrel is hit by a car. It flies off with a speed of 99.0 m/s at an angle of 45 degrees above the horizontal. It lands on the flat roof of a 25.0 m  tall building. Determine a: how long the squireel was in the air. B: the maximum height above the ground. And C the horizontal distance it travels before it lands on the building?

To solve this problem, we can break the squirrel’s motion into horizontal and vertical components, treating it as a projectile motion problem.

Given dataTo solve this problem, we can break the squirrel’s motion into horizontal and vertical components, treating it as a projectile motion problem.

Given 
- Initial speed, \( v_0 = 99.0 \, \text{m/s} \)
- Angle of projection, \( \theta = 45^\circ \)
- Height of the building, \( h = 25.0 \, \text{m} \)
- Acceleration due to gravity, \( g = 9.81 \, \text{m/s}^2 \)

### A) Time in the Air

We can use the kinematic equation for vertical motion to calculate the time the squirrel spends in the air. The vertical displacement \( \Delta y \) between the initial position (ground) and the final position (roof of the building) is -25.0 m (since it is lower than its maximum height).

The vertical motion is described by:
\[
\Delta y = v_{0y} t - \frac{1}{2} g t^2
\]
where:
\[
v_{0y} = v_0 \sin \theta
\]
Substituting known values:
\[
\Delta y = -25.0 \, \text{m}, \, v_0 = 99.0 \, \text{m/s}, \, \theta = 45^\circ, \, g = 9.81 \, \text{m/s}^2
\]

This gives us a quadratic equation to solve for time \( t \).

### B) Maximum Height Above the Ground

The maximum height occurs when the vertical velocity becomes zero. The equation for maximum height is:
\[
h_{\text{max}} = \frac{(v_{0y})^2}{2g}
\]

We will first calculate \( v_{0y} \) and then use it to find \( h_{\text{max}} \).

### C) Horizontal Distance

The horizontal distance traveled is given by:
\[
x = v_{0x} \cdot t
\]
where:
\[
v_{0x} = v_0 \cos \theta
\]
We will use the time of flight (calculated in part A) to determine the horizontal distance.

Let me calculate each part step by step.

A squirrel is hit by a car. It flies off with a speed of 99.0 m/s at an angle of 45 degrees above the horizontal. It lands on the flat roof of a 25.0 m tall building. Determine a: how long the squirrel was in the air. b: the maximum height above the ground. And c: the horizontal distance it travels before it lands on the building?

Solve a projectile motion problem involving a squirrel flying off at 99.0 m/s at a 45-degree angle. Calculate the time in the air, maximum height, and horizontal distance using kinematic equations. Suitable for high school students studying Grades 11-12.

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