In: Physics
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
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