A projectile is launched with an initial velocity of 30 m/s at an angle of 45 de

₹0.0

Question: A projectile is launched with an initial velocity of 30 m/s at an angle of 45 degrees. What is the maximum height reached?

Options:

Correct Answer: 22.5 m

Solution:

Maximum height (H) = (u² * sin²θ) / (2g) = (30² * (1/2)) / (2 * 9.8) = 22.5 m.

A projectile is launched with an initial velocity of 30 m/s at an angle of 45 degrees. What is the maximum height reached?

A projectile is launched with an initial velocity of 30 m/s at an angle of 45 degrees. What is the maximum height reached?

Step 1: Identify the initial velocity (u) of the projectile, which is given as 30 m/s.
Step 2: Identify the angle of launch (θ), which is given as 45 degrees.
Step 3: Convert the angle from degrees to radians if necessary, but for this calculation, we can use the sine of 45 degrees directly.
Step 4: Calculate the sine of the angle: sin(45 degrees) = √2/2 = 1/√2 ≈ 0.7071. However, for simplicity, we can use sin(45 degrees) = 1/2 in the formula.
Step 5: Use the formula for maximum height (H): H = (u² * sin²θ) / (2g).
Step 6: Substitute the values into the formula: H = (30² * (1/2)) / (2 * 9.8).
Step 7: Calculate 30², which is 900.
Step 8: Calculate (1/2) * 900 = 450.
Step 9: Calculate 2 * 9.8, which is 19.6.
Step 10: Divide 450 by 19.6 to find the maximum height: H = 450 / 19.6 ≈ 22.5 m.

Projectile Motion – The study of the motion of an object that is launched into the air and influenced only by gravity and its initial velocity.
Maximum Height Calculation – The formula used to calculate the maximum height of a projectile based on its initial velocity and launch angle.
Trigonometric Functions – Understanding the use of sine and cosine functions to resolve the initial velocity into vertical and horizontal components.