Part A Determine the time taken by the projectile to hit point P at ground level

ID: 1655239 • Letter: P

Question

Part A

Determine the time taken by the projectile to hit point P at ground level.

t =

Part B

Determine the distance X of point P from the base of the vertical cliff.

X =

Part C

At the instant just before the projectile hits point P , find the horizontal and the vertical components of its velocity.

vx , vy =

Part D

At the instant just before the projectile hits point P , find the magnitude of the velocity.

v =

Part E

At the instant just before the projectile hits point P , find the angle made by the velocity vector with the horizontal.

Part F

Find the maximum height above the cliff top reached by the projectile.

ymax =

35.0° h=115m

(A) as object hit the ground,

vertical displacement, y = 0 - 115 = - 115 m

ay = - 9.8 m/s^2

v0y = 63 sin35 = 36.1 m/s

Applying y = v0y t + ay t^2 / 2

- 115 = 36.1 t - 4.9 t^2

4.9 t^2 - 36.1t - 115= 0

t = 9.77 sec

(B) X = (63 cos35) (9.77)

X = 504 m

vy = v0y + at = 36.1 - (9.8 x 9.77)

vy = - 59.6 m/s

(d) magnitude = sqrt(vx^2 + vy^2) =79 m/s

(e) theta = tan^-1(59.6 / 51.6) = 49 deg below the horizontal.

(f) at maximum h, vy = 0

0^2 - 36.1^2 = 2(-9.8) (h)

h = 66.5 m above the cliff