Question

The caveman, Thug, was using an atlatl to throw a spear at his prey. On one throw he threw it at 38.2 degrees with the ground at 28.8 m/s.

What was the spear’s apogee height?
Assuming the spear lands at the same height it is thrown from, how much time did it spend in the air?
Include step by step explanation please so I can learn it better :D

Answer 1

To find the spear's apogee height, use the kinematic equation for vertical motion. The time it spent in the air can be calculated using the equation for time of flight. Substituting the given values and solving the equations will give the answers.

Step-by-step explanation:

To find the spear's apogee height, we can use the kinematic equation for vertical motion. The equation is:

displacement = (initial velocity * time) + (0.5 * acceleration * time^2)

In this case, the displacement is 0 m since the spear lands at the same height it is thrown from. The initial velocity is the vertical component of the throwing velocity, which can be calculated using the equation:

initial velocity = throwing velocity * sin(angle)

Substituting the given values, we have:

0 = (28.8 * sin(38.2)) * t - (0.5 * 9.8 * t^2)

Simplifying the equation gives us a quadratic equation:

0.5 * 9.8 * t^2 - (28.8 * sin(38.2)) * t = 0

We can solve this equation to find the value of t. The apogee height is then calculated using the equation:

apogee height = initial velocity * t + (0.5 * acceleration * t^2)

Substituting the calculated value of t and the given values, we can find the apogee height.

To find the time spent in the air, we can use the equation:

time = (2 * initial velocity * sin(angle)) / acceleration

Substituting the given values, we can find the time spent in the air.