147k views
4 votes
A grasshopper jumps straight up from the ground with an initial vertical velocity of 8 feet per second. a. Write an equation that gives the height (in feet) of the grasshopper as a function of the time (in seconds) since it leaves the ground. b. After how many seconds is the grasshopper 1 foot off the ground?

User Ntan
by
9.3k points

1 Answer

5 votes

Answer:

The grasshopper will be at 1 foot after 1.50 seconds.

Explanation:

a). A grasshopper jumps straight up with an initial vertical velocity = 8 feet per second

From the equations of vertical motion,


h=ut-(1)/(2)gt^(2)

Here h = height of the grasshopper at the time 't'

u = initial velocity

g = Acceleration due to gravity

t = duration or time

Now we plug in the value of initial velocity in this equation.


h=8t-(1)/(2)gt^(2)

b). In this part we have to calculate the time when the grasshopper is 1 foot off the ground.

from the expression of part (a),


1=8t-(1)/(2)gt^(2)


2=16t-(9.8)t^(2)


-(9.8)t^(2)+16t-2=0

t =
\frac{-16\pm \sqrt{(16)^(2)-4(-9.8)(-2)}}{2(-9.8)}

=
\frac{-16\pm \sqrt{(16)^(2)-78.4}}{2(-9.8)}

=
(-16\pm 13.32)/(-19.6)

= 1.50, (-0.14) seconds

But the time can not be negative, so the grasshopper will be at 1 foot after 1.50 seconds.

User Jichao
by
8.1k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories