An arrow is shot at an angle 20 degrees from the horizontal. If its height is increasing at 250 km/hr, how fast is the arrow itself going? (Not the horizontal speed, but it's actual diagonal speed.)

Answer 1

Since the arrow is shot at an angle of 20 degrees from the horizontal, we can find the initial velocity in each direction:

V_x = V_i Cos(\theta)

V_y = V_i Sin(\theta)

where V_i is the total initial velocity.

If the height of the arrow is increasing at a rate of 250 km/hr, noting that a change in position over a change in time is nothing but velocity, we have V_y = 250 km/hr. We can solve for the total initial velocity:

V_i = V_y / Sin(\theta) = 250 / Sin(20 Degrees) = 730.951 km/hr

I hope this helps, feel free to reach out with any other questions.