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In: Physics

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 = = 31o

Initial horizontal velocity of the rock = Vx0 = V0Cos

Initial vertical velocity of the rock = Vy0 = 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 = Vx1 = 26.5 m/s

Vertical velocity of the rock at the highest point = Vy1 = 0 m/s

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

Vx1 = Vx0

Vx0 = 26.5 m/s

V0Cos = 26.5

V0Cos(31) = 26.5

V0 = 30.916 m/s

Vy0 = V0Sin

Vy0 = (30.916)Sin(31)

Vy0 = 15.923 m/s

Maximum height attained by the rock = H

Vy12 = Vy02 + 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 3 months ago
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