Question

A projectile is launched from the ground with a speed of 30 m/s at a projection angle of 45 degrees. What is the maximum height reached? What is the range?

Options:
A) 15 m, 45 m
B) 30 m, 60 m
C) 45 m, 90 m
D) 60 m, 120 m

Answer 1

The maximum height and range of a projectile launched at 30 m/s at a 45-degree angle are closest to option C, with a calculated maximum height of approximately 45.9 m and range of approximately 91.8 m.

Step-by-step explanation:

Maximum Height and Range of a Projectile:

A projectile launched from the ground at a speed of 30 m/s and a projection angle of 45 degrees will reach a certain maximum height and range. To find these, we can use the equations of motion for projectile motion. Assuming acceleration due to gravity (g) is 9.81 m/s2 and neglecting air resistance, we can calculate maximum height (H) using the formula:

H = (v_i2 * sin2(θ)) / (2 * g)
Where v_i is the initial velocity and θ is the angle of projection. For the range (R), we use:

R = (v_i2 * sin(2*θ)) / g
After substituting the numerical values and performing the calculations for a projection angle of 45 degrees:

• Maximum height: H = (30 m/s)2 * sin2(45°) / (2 * 9.81 m/s2) = 45.9 m (approx).
• Range: R = (30 m/s)2 * sin(90°) / 9.81 m/s2 = 91.8 m (approx).

However, since we must choose from the given options, option C, which states a maximum height of 45 m and a range of 90 m, is the closest correct option.