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A cricket batsman hits a ball at a speed of 27m/s at an angle of 60 degrees to the horizontal. How far away would you have to stand in order to catch it (assuming you want to catch it just before it hits the ground)?

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MathPhys

Answer:

64.4 m

Explanation:

First, find how long it takes to land.  Given in the y direction:

Δy = 0 m

v₀ = 27 m/s sin 60° ≈ 23.4 m/s

a = -9.8 m/s²

Find: t

Δy = v₀ t + ½ at²

0 m = (23.4 m/s) t + ½ (-9.8 m/s²) t²

t = 4.77 s

Next, find how far it travels in that time.  Given in the x direction:

v₀ = 27 m/s cos 60° = 13.5 m/s

a = 0 m/s²

t = 4.77 s

Find: Δx

Δx = v₀ t + ½ at²

Δx = (13.5 m/s) (4.77 s) + ½ (0 m/s²) (4.77 s)²

Δx = 64.4 m

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