Question

A boy uses a sling to throw a rock a distance of 100 m. If the rock is in the air for 5 seconds, find each of the following:

a) How fast is the rock initially traveling horizontally?

b) How fast is the rock initially traveling vertically?

c) How high does the rock get?

d) At what angle does it hit the ground?

Answer 1

a.)

Time period of flight is given by,

T = 2*u*sinA/g

range of projection is given by,

R = u^2*2*sinA*cosA/g

Given, R = 100 m

T = 5 sec.

u = initial velocity

A = angle of projection

So, by dividing both equation,

R/T = u*cosA =  initially horizontal velocity(ux)

ux = R/T = 100/5

ux = 20 m/s

b.)

from time period formula,

u*sinA =  initially vertical velocity(uy) = T*g/2

here, g = 9.81 m/s^2

then, uy = 5*9.81/2

uy = 24.525 m/s

c.)

height of projection = Hmax = uy^2/(2*g)

Hmax = 24.525^2/(2*9.81)

Hmax = 30.66 m

d.)

By kinematics law in vertical direction,

vy - uy = ay*t

here, ay = -g

t = 5 sec.

So, vy = uy + (-g)*t = 24.525 + (-9.81)*5

vy = v*sinA = -24.525 m/s

now, vx = v*cosA = ux = 20 m/s

by dividing both equation,

angle of hitting the ground(A) = angle of hitting the ground = arctan(vy/vx)

A = arctan(-24.525/20)

A = -50.80 deg

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