Question

Use principles of physics to solve the problem and then verify your answer using the simulation. Assume that the acceleration due to gravity has a magnitude of g = 9.80 m/s2. If the range of the projectile is 5.96 m, the time-of-flight is T = 1.20 s, and air resistance is turned off, determine the following. A. What is the launch angle of the projectile? B. What is the initial speed of the projectile? C. Express the maximum height reached by the projectile in terms of g and T (the time-of-flight). h_max = "Please show detailed work" I am trying to figure out how to do this for future problems."

Answer 1

let the initial speed of launch be "v" and angle of launch be ""

consider the motion along X-direction ":

X = horiontal range = 5.96 m

t = time of flight = 1.20 s

v_ox = velocity along x-direction = v Cos = ?

using the equation

X = v_ox t

5.96 = (v Cos) (1.20)

v Cos = 4.96 eq-1

consider the motion along Y-direction ":

Y = vertical displacement = 0 m

t = time of flight = 1.20 s

v_oy = velocity along y-direction = v Sin = ?

using the equation

Y = v_oy t + (0.5) a t²

0 = (v Sin) (1.20) + (0.5) (-9.8) (1.20)²

v Sin = 5.88 eq-2

dividing eq-2 by eq-1

v Sin/(v Cos) = 5.88/4.96

= 49.83

B)

using eq-1

v Cos = 4.96   

v Cos49.83 = 4.96   

v = 7.63 m/s

c)

consider the motion along Y-direction ":

Y = vertical displacement = ?

a = acceleration = - 9.8

v_oy = initial velocity = v Sin = 7.63 Sin49.83 = 5.83 m/s

v_fy = final velocity at the maximum height = 0 m/s

using the equation

v_fy² = v_oy² + 2 a Y

(0)² = (5.83)² + 2 (-9.8) Y

Y = 1.73 m