Question

A cannonball is launched diagonally with an initial horizontal speed of 51.0m/s
and an initial vertical speed of 24.0m/s. Label the hypotenuse, opposite side and
adjacent side, and determine all unknowns.
m/s
initial speed:
initial horizontal speed:
initial vertical speed:
m/s
m/s
At what angle () was the cannonball launched?

Answer 1

• initial horizontal speed: 51.0 m/s

• initial vertical speed: 24.0 m/s

• initial speed: √((51.0 m/s)² + (24.0 m/s)²) ≈ 56.4 m/s

• angle: tan(θ) = (24.0 m/s) / (51.0 m/s)   →   θ ≈ 25.2º

Answer 2

Using Pythagoras, the initial speed and the launch angle of the cannon ball are 56.36 m/s and 25.20° respectively.

The initial speed can be obtained using length of the diagonal :

v² = 51² + 24²

v² = 2025

v = √3177

v = 56.36 m/s

The launch angle, θ :

• Tanθ = opposite / Adjacent

θ = tan¯¹(24/51)

θ = tan¯¹(0.4705)

θ = 25.20°

Hence, the angle of launch is 25.20°

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