The distance s (in m) above the ground for a projectile fired vertically upward with a velocity of 4[a] m/s as a function of time t (in s ) is given by s=4[a]t−4.[b]t2..

a=3, b=7

find latex: t for latex: v=0, find find latex: v for latex: t=4, find find latex: v for latex: t=5. what conclusions can you draw?

find the answers to these questions. what conclusions can you draw?

Answers:

a) 1.224 s

b) -27.2 m/s

c) -37 m/s

Step-by-step explanation:

According to the given information the distance is given by:

(1)

In additio, since the projectile was fired vertically we can use the following equation:

(2)

Where:

is the final velocity

is the initial velocity

is the acceleration due gravity

is the time

Knowing this, let's begin:

a) Find  for

Using (2):

(3)

(4)

(5)

(6)

b) Find for

In this case we have to find :

(7)

(8)

c) Find for

(9)

(10)

Conclusions:

The time we found in a) when is at the maximum height of the projectile, just before going down. That is why in parts b) and c) when time is and the velocity is negative, because it is directed downwards.