Question

What is the maximum height reached by the T-shirts launched by cheerleaders at a football game when the initial upward velocity is 40 feet per second instead of 30 feet per second?

Answer 1

To find the maximum height reached by the T-shirts launched by cheerleaders, we can use the following kinematic equation, which describes the motion of an object under constant acceleration (in this case, the acceleration due to gravity):

\[
h = v_i t + \frac{1}{2} a t^2
\]

where:
- \( h \) is the maximum height,
- \( v_i \) is the initial velocity,
- \( a \) is the acceleration (which will be negative due to gravity), and
- \( t \) is the time of flight until reaching the maximum height.

However, it’s often more straightforward to use the following formula to compute the maximum height directly when you know the initial velocity:

\[
H = \frac{v_i^2}{2g}
\]

where:
- \( H \) is the maximum height,
- \( v_i \) is the initial velocity (in this case, 40 feet per second), and
- \( g \) is the acceleration due to gravity (approximately 32 feet per second squared).

Now, substituting \( v_i = 40 \) feet per second and \( g = 32 \) feet per second squared into the equation:

\[
H = \frac{(40)^2}{2 \times 32} = \frac{1600}{64} = 25 \text{ feet}
\]

Thus, the maximum height reached by the T-shirts launched at an initial velocity of 40 feet per second is **25 feet**.