Only given displacement vector and initial speed, solve for theta

[i_heart_you]

Homework Statement

A ball is thrown with a speed of 70m/s and hits the top of a wall which is 20m tall and 100m away. Find the angle that the ball was thrown at

Homework Equations

d= V0xt + 1/2 a t^2
a = Vf-V0/t
sin^2(theta) = 1 - cos^2 (theta)

The Attempt at a Solution

I found the initial velocity in terms of theta V= 70cos(theta) x + 70sin(theta) y
the part I'm stuck on is apparently we are supposed to find the time from the horizontal displacement somehow. That i am stuck on because it seems like a i have too many variables and not enough information. any help is appriciated

 

[hotvette]

I think you have all the information you need. You can write separate equations for the x and y displacement in terms of theta and t. This is two equations and two unknowns.

 

[tomcue]

I would approach this problem by first drawing a diagram to visualize the situation. From the given information, we know that the ball has a horizontal displacement of 100m and a vertical displacement of 20m. We also know the initial speed, 70m/s, which can be broken down into its horizontal and vertical components using trigonometric functions.

Using the equation d= V0xt + 1/2 a t^2, we can set up two equations: one for the horizontal displacement and one for the vertical displacement. Since the acceleration in the horizontal direction is zero, we can simplify the horizontal equation to d= V0xt. For the vertical equation, we can use the acceleration due to gravity, 9.8m/s^2, and the fact that the final vertical velocity is zero at the top of the wall.

By solving these equations simultaneously, we can find the time it takes for the ball to reach the top of the wall. Once we have the time, we can use the equation a = Vf-V0/t to find the vertical component of the initial velocity. Then, we can use the inverse trigonometric function to solve for the angle theta.

In summary, to solve for theta, we need to use the given displacement vector, initial speed, and the equations of motion to find the time and initial vertical velocity. From there, we can use inverse trigonometric functions to solve for theta. It is important to carefully consider the given information and equations to make sure we are using the correct variables and equations to solve the problem.