A stoane propelled from a catapult with a speed of 60ms-1 attains a height of 120m. Calculate the time of flight, the angle of projection, the range
Recall your basic trajectory formulas.
height = 60 sinθ t - 1/2 gt^2
max height = v^2/2g sin^2θ
range = v^2/g sin2θ
a. Y^2 = Yo^2 + 2gh = 0,
Yo^2 + (-19.6)*120 = 0,
Yo = 48.5 m/s. = vertical comp. of initial velocity.
Y = Yo + g*Tr = 0,
48.5 + (-9.8)Tr = 0,
Tr = 5.0s = rise time.
Tf = Tr = 5 s. = Fall time.
T = Tr+Tf = 5 + 5 = 10s. = Time of flight.
b. Vo*sin A = Yo = 48.5,
60*sinA = 48.5,
A = 53.9o = angle of projection.
c. Vo = 60m/s[53.9o],
Range = Vo^2*sin(2A)/g = 60^2*sin(107.8)/9.8 = 350 m.