A basketball is thrown from the ground into the air at an angle of 30 degrees to the horizontal. If this object reaches a maximum height of 5.75m, at what velocity was it thrown?
How am i suppose to do this question if no velocity is given? I need help. I have a test tomm.
To solve this problem, you can use the equations of motion for projectile motion. Let's break down the process step by step:
Step 1: Identify given information:
- The angle of projection (angle with respect to the horizontal) is 30 degrees.
- The maximum height reached by the basketball is 5.75m.
Step 2: Determine the equation to use:
For projectile motion, we can use the equation for the maximum height reached by an object:
Hmax = (v^2 * sin^2θ) / (2 * g)
where:
- Hmax is the maximum height
- v is the initial velocity of the object
- θ is the angle of projection
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
Step 3: Solve for the initial velocity (v):
Rearranging the equation, we get:
v = sqrt((Hmax * 2 * g) / sin^2θ)
Substituting the given values:
v = sqrt((5.75 * 2 * 9.8) / sin^2(30))
Step 4: Calculate the velocity:
Using a scientific calculator, evaluate the expression to find the value of v.
v ≈ 14.00 m/s
Therefore, the basketball was thrown with an initial velocity of approximately 14.00 m/s.
Note: It's essential to have a clear understanding of the concepts of projectile motion and the equations involved in solving such problems. Make sure to double-check the values and units to ensure correct calculations.