A launched rocket has an altitude in meters, given by the polynomial h+vt-4.9^2, h is the height in meters v is the velocity in meters per second and t is the number of seconds for which it takes the rocket to become airborne. If the rocket is launched from the top of a tower that is 100 meters and the initial speed is 60 meters per second, what will its height be after 4 seconds rounded to the nearest tenth?
h = 100 + Vo*t + 0.5*gt^2.
h = 100 + 60*4 + 0.5*(-9.8)4^2,
h = 100 + 240 - 78.4 = 261.6m above ground.
h = 261.6 - 100 = 161.6m above the tower.
To find the height of the rocket after 4 seconds, we need to substitute the values of h, v, and t into the given polynomial equation.
Given:
h = height of the tower = 100 meters
v = initial velocity = 60 meters per second
t = time taken for the rocket to become airborne = 4 seconds
We can substitute these values into the equation h + vt - 4.9t^2 and calculate the height of the rocket.
Plugging in the values:
h + vt - 4.9t^2 = 100 + (60 * 4) - 4.9 * (4^2)
Simplifying:
h + vt - 4.9t^2 = 100 + 240 - 4.9 * 16
= 100 + 240 - 78.4
= 340 - 78.4
= 261.6
The height of the rocket after 4 seconds is 261.6 meters rounded to the nearest tenth.