Question

the equation above expresses the approximate height h, in meters, of a homemade rocket t seconds after it is launched vertically upward from the ground with an initial velocity of 35 meters per second. after approximately how many seconds will the rocket hit the ground? a 5 b 6 c 7 d 7.5 e 8

Explanation:

Step1: Set height \( h = 0 \)

When the rocket hits the ground, its height \( h = 0 \). So we set the equation \( - 6.9t^{2}+35t=0 \).

Step2: Factor out \( t \)

Factor the left - hand side of the equation: \( t(-6.9t + 35)=0 \).
This gives us two solutions for \( t \) from the zero - product property \( ab = 0\) implies \(a = 0\) or \(b = 0\).
One solution is \( t = 0\) (corresponds to the time of launch).
For the other solution, we solve \( - 6.9t+35 = 0\).
First, add \(6.9t\) to both sides: \(35=6.9t\).
Then, divide both sides by \(6.9\): \(t=\frac{35}{6.9}\approx5.07\approx5\).

Answer:

A. 5