Question

HELP

A toy rocket is launched from a 2.1 m high platform in such a way that its height, h (in meters), after t seconds is given by the
equation h = -4.9t² + 14.0t+2.1. How long will it take for the rocket to hit the ground?

Answer 1

3 seconds

Explanation:

The height of the rocket when it hits the ground will be zero meters.

Therefore, set the equation to zero and solve for t by using the quadratic formula.

Quadratic Formula

`x=(-b \pm √(b^2-4ac) )/(2a)\quad\textsf{when }\:ax^2+bx+c=0`

Given equation:

`-4.9t^2+14t+2.1=0`

Therefore:

`a=-4.9, \quad b=14, \quad c=2.1`

Substitute the values into the quadratic formula:

`\implies t=(-14 \pm √(14^2-4(-4.9)(2.1)))/(2(-4.9))`

`\implies t=(-14 \pm √(196+41.16))/(-9.8)`

`\implies t=(-14 \pm √(237.16))/(-9.8)`

`\implies t=(-14 \pm15.4)/(-9.8)`

Therefore:

`\implies t=(-14 +15.4)/(-9.8)=(1.4)/(-9.8)=-(1)/(7)`

`\implies t=(-14-15.4)/(-9.8)=(-29.4)/(-9.8)=3`

As time is positive, t = 3 s only.

Therefore, it will take 3 seconds for the rocket to hit the ground.