A circus performer decides to take his human cannonball act to the extreme. After being shot from a cannon, he soars over three ferris wheels and into a net. Assume that he is launched with a speed of 26.5m/s at an angle of 53.0 degrees, what angle does he make with the vertical when he hits the net?
I got 37 degrees, I don't know if the angle from the horizontal from launch is the same angle he makes with the horizontal when he lands. If it is i just subtracted 53 from 90 degrees
I agree with your answer.
To determine the angle the circus performer makes with the vertical when he hits the net, let's break down the problem step by step:
1. Start by breaking down the initial velocity into its horizontal and vertical components. The initial velocity can be separated into two vectors: Vx (horizontal component) and Vy (vertical component).
Vx = V * cos(theta)
Vy = V * sin(theta)
where V is the magnitude of the initial velocity (26.5 m/s) and theta is the launch angle (53.0 degrees).
2. Calculate the time it takes for the circus performer to reach the net. Since the motion is purely vertical, we can use the equation:
Vertical displacement (dy) = Vy * t + (1/2) * g * t^2
where dy is the vertical displacement, Vy is the vertical component of the initial velocity, t is the total time of flight, and g is the acceleration due to gravity (-9.8 m/s^2).
As the circus performer starts and ends at the same vertical position, the vertical displacement is zero (dy = 0). Solving the equation for t will give us the total time of flight.
3. Once you find the time of flight, substitute it into the horizontal displacement equation:
Horizontal displacement (dx) = Vx * t
This equation will give us the horizontal distance traveled by the circus performer before hitting the net.
4. Finally, calculate the angle the performer makes with the vertical when he hits the net. This angle can be found using the tangent function:
tan(angle) = dx / dy
where dx is the horizontal displacement and dy is the vertical displacement.
Now, plug in the values you have and solve the equations step by step to find the angle the performer makes with the vertical when he hits the net.