Question

A projectile is projected from the origin with a velocity of 30

Answer 1

For this we will use kinematic equations.

We need the time of flight to compute the range.

With the given information, the most useful formula is:

Δy=v0yt−g2t2

Because our equation is taking only vertical motion into account,

v0y=30sin(45)

Because we are looking for the range of the object,

Δy=0

This leaves us with only one unknown:  t

0=30sin(45)t−g2t2

g2t2=30sin(45)t

g2t=30sin(45)

t=60gsin(45)

For horizontal distance, the formula we need is:

Δx=v0xt

Because we are taking into account the horizontal range,

v0x=30cos(45)

In substituting our derived values into the equation we can see that:

Δx=30cos(45)∗60gsin(45)

Range=30cos(45)∗60gsin(45)