A stone propelled from a catapult with a speed of 50 MS^-1 attains a height of 100 m. Calculate:

Question

a. the time of flight.
b. the angle of projection.
c. the range attained.

Answer 1

a. To calculate the time of flight, we can use the equation of motion for vertical motion:

final velocity squared = initial velocity squared + 2 * acceleration * displacement

The final velocity is 0 m/s at the highest point of the projectile's motion. The initial velocity is 50 m/s. The acceleration due to gravity is -9.8 m/s^2 (taking downward as negative), and the displacement is 100 m (upwards).

0 = 50^2 + 2 * (-9.8) * 100

0 = 2500 - 1960 * 100

1960 * 100 = 2500

196000 = 2500

The equation is impossible, so there must be an error in the given parameters or assumptions.

b. To calculate the angle of projection, we can use the equation for the maximum height of a projectile:

maximum height = (initial velocity squared * sin^2(angle of projection))/(2 * acceleration due to gravity)

We can rearrange this equation to solve for the angle of projection:

sin^2(angle of projection) = (maximum height * 2 * acceleration due to gravity) / (initial velocity squared)

angle of projection = arcsin(sqrt((maximum height * 2 * acceleration due to gravity) / (initial velocity squared)))

angle of projection = arcsin(sqrt((100 * 2 * 9.8) / (50^2)))

angle of projection = arcsin(sqrt((1960) / (2500)))

Using a calculator, the angle of projection is approximately 48.2 degrees.

c. To calculate the range attained, we can use the equation of motion for horizontal motion:

range = initial velocity * time of flight

As we were unable to calculate the time of flight in part a, we cannot calculate the range with the given information.