A catapult launches a rock at a 31° angle with respect to the horizontal. Find the...

A catapult launches a rock at a 31° angle with respect to the horizontal. Find the maximum height attained if the speed of the rock at its highest point is 26.5 m/s.
m

Solutions

Expert Solution

Gravitational acceleration = g = -9.81 m/s²

Initial velocity of the rock = V₀

Angle of launch = = 31^o

Initial horizontal velocity of the rock = V_x0 = V₀Cos

Initial vertical velocity of the rock = V_y0 = V₀Sin

Velocity of the rock at the highest point = V₁ = 26.5 m/s

At the highest point the velocity of the rock will be horizontal.

Horizontal velocity of the rock at the highest point = V_x1 = 26.5 m/s

Vertical velocity of the rock at the highest point = V_y1 = 0 m/s

There is no horizontal force acting on the rock therefore the horizontal velocity of the rock remains constant.

V_x1 = V_x0

V_x0 = 26.5 m/s

V₀Cos = 26.5

V₀Cos(31) = 26.5

V₀ = 30.916 m/s

V_y0 = V₀Sin

V_y0 = (30.916)Sin(31)

V_y0 = 15.923 m/s

Maximum height attained by the rock = H

V_y1² = V_y0² + 2gH

(0)² = (15.923)² + (2)(-9.81)H

H = 12.92 m

Maximum height attained by the rock = 12.92 m

genius_generous answered 1 month ago

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