b) What was the initial speed of the toy car? A projectile is shot from the edge

Question

b) What was the initial speed of the toy car? A projectile is shot from the edge of a cliff 115 m above ground level with an initial speed of vo 70 m/s at an angle of 35° with the horizontal, as shown in the figure on the next page. a) Determine the time taken by the projectile to hit point P at ground level. b) Determine the range X of the projectile as measured from the base of the cliff. c) At the instant just before the projectile hits point P, find the horizontal and vertical 3. components of its velocity d) At the instant just before the projectile hits point P, find the magnitude and direction of the velocity vector.

Explanation / Answer

here,

v0 = 70 m/s

theta = 35 degree

height , h0 = 115 m

a)

let the time taken to hit the point P be t

h = v0y * t + 0.5 * g * t^2

h = - v0 * sin(35) * t + 0.5 * g * t^2

115 = - 70 * sin(35) * t + 0.5 * 9.81 * t^2

solving for t

t = 10.4 s

b)

the range X = v0x * t

X = v0 * cos(theta) * t

X = 70 * cos(35) * 10.4 = 596.3 m

c)

final horizontal velocity , vx= v0x = v0 * cos(theta) = 57.3 m/s

final vertical velocity , vy = v0y + g * t

vy = - v0 * sin(theta) + g * t

vy = - 70 * sin(35) + 9.81 * 10.4

vy = 61.9 m/s

d)

magnitude of velocity , |v| = sqrt(vx^2 + vy^2)

|v| = 84.4 m/s

direction , theta = arctan(vy/vx) = 47.2 degree below the horizontal

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