Question

If a ball launched at an angle of 10.0 degrees above horizontal from an initial height of 1.50 meters has a final horizontal displacement of 3.00 meters, what is its launch velocity? Show your work.

Answer 1

To find the launch velocity of the ball, we can use the equations of projectile motion. The horizontal displacement of the ball is given as 3.00 meters. By considering the vertical displacement and using the equations of projectile motion, we can solve for the launch velocity.

Step-by-step explanation:

To find the launch velocity of the ball, we can use the equations of projectile motion. The horizontal displacement of the ball is given as 3.00 meters. To find the launch velocity, we need to consider the vertical displacement of the ball as well.

Using the vertical displacement, we can find the time of flight of the ball using the equation y = ut + (1/2)at^2, where y is the vertical displacement, u is the initial vertical velocity, t is the time of flight, and a is the acceleration due to gravity.

Once we have the time of flight, we can use the equation x = ut, where x is the horizontal displacement, u is the launch velocity, and t is the time of flight. By substituting the given values into the equations, we can solve for the launch velocity.

Let's assume the acceleration due to gravity as -9.8 m/s^2. Plugging in the values, we get:

1.5 = u*sin(10)*t - (1/2)*9.8*t^2

3.00 = u*cos(10)*t

Solving these two equations simultaneously will give us the launch velocity.