Abody is projected from the ground at an angle of 30° with the horizontal at an initial speed of 128 ft/s. ignoring air friction, determine:

a) in how many seconds it will strike the ground.

b) how high it will go.

c) what its range will be.

Answer

given,

v = 128 ft/s

angle made with horizontal = 30°

now,

horizontal component of velocity

vx = v cos θ = 128 x cos 30° = 110.85 ft/s

vertical component of velocity

vy = v sin θ = 128 x sin 30° = 64 m/s

time taken to strike the ground

using equation of motion

v = u + at

0 =-64 -32 x t

t = 2 s

total time of flight is equal to

T = 2 t = 2 x 2 = 4 s

b) maximum height

using equation of motion

 v² = u² + 2 a h

 0 = 64² - 2 x 32 x h

 64 h = 64²

  h = 64 ft

c) range

R = v_x × time of flight

R = 110.85 × 4

R = 443.4 ft

the maxium height is 34m/s