Question

The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground?

30 meters
40 meters
50 meters
60 meters ​

Answer 1

40 meters

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

`s=ut+(1)/(2)at^2\\\Rightarrow u=(s-(1)/(2)at^2)/(t)\\\Rightarrow u=(90-(1)/(2)* 9.81* 3^2)/(3)\\\Rightarrow u=15.285\ m/s`

u = 15.285 m/s

`s=ut+(1)/(2)at^2\\\Rightarrow s=15.285* 2+(1)/(2)* 9.81* 2^2\\\Rightarrow s=50.19\ m`

The ball has fallen 50.19 m from the top of the building.

So, the ball is 90-50.19 = 39.81 = 40 meters off the ground

Answer 2

A. 30 meters

Explanation:

Let's find the answer.

The problem established a quadratic relationship between height (h) and time (t), then we can establish:

h(t)=K*t where 'K' is a coefficient.

Because an experiment was done, we can find 'K' as follows:

h(t)=K*t

90meters=K*(3seconds)

90meters/3seconds=K

30m/s=K

Now we can solve the problem, so for 2 seconds:

h(t)=K*t

h(t)=(30m/s)*(2s)

h(t)=60m

But notice that the obtained 60 meters are the distance traveled in 2 seconds from the top the building to the ground. So 'how far from the ground' can be calculated as:

(far from the ground) = (total building height) - (distance traveled in 2s)

(far from the ground) = 90m - 60m = 30m

In conclusion, after 2 seconds, the ball is 30 meters far from the ground. The answer in then A. 30 meters.