A squash ball hits a wall at a height of 4m and a distance of 6m away.
If the ball left the racquet with
a speed of 15m/s, with what angle did the player hit the ball?
I have applied concepts of projectile motion and tried kinematic equations. However I have two unknowns that I don't know how to solve for (Time and Angle).
I am wondering from what height it was hit by the player.
Yes, that's true as well, the actual change in the vertical component isn't known. Is this question solvable?
To find the angle at which the player hit the ball, you can use the concept of projectile motion and kinematic equations. Here's how you can approach the problem:
Step 1: Analyze the motion horizontally and vertically.
The ball's horizontal motion is constant, as there are no forces acting on it in that direction. The ball's vertical motion is influenced by gravity.
Step 2: Break down the initial velocity.
The ball left the racquet with a speed of 15 m/s, which can be broken down into horizontal and vertical components. Let's call the angle at which the ball was hit θ.
The horizontal component (Vx) can be found using trigonometry:
Vx = 15 m/s * cos(θ)
The vertical component (Vy) can also be found using trigonometry:
Vy = 15 m/s * sin(θ)
Step 3: Analyze the vertical motion.
For the vertical motion, we can use the following equation:
y = yo + Vyo * t - 0.5 * g * t^2
where:
- y is the vertical displacement (4 m)
- yo is the initial vertical position (0 m)
- Vyo is the initial vertical velocity (Vy)
- g is the acceleration due to gravity (9.8 m/s^2)
- t is the time of flight
Step 4: Analyze the horizontal motion.
For the horizontal motion, we know that the wall is 6 m away from the starting point. The horizontal distance traveled (x) can be calculated using the equation:
x = Vx * t
Step 5: Solve the system of equations.
Now, we have two equations and two unknowns (t and θ). You can substitute the values of Vx and Vy from steps 2 and 3 into the equations for y and x. Then, solve the equations simultaneously to find the time of flight (t) and the angle (θ) at which the ball was hit.
Step 6: Calculate the angle.
Once you find the value of θ, use inverse trigonometric functions to calculate the angle. For example, if you find that sin(θ) = 0.6, you would calculate θ = arcsin(0.6).
By following these steps, you should be able to solve for the angle at which the player hit the ball.