Answer:
Step-by-step explanation:
Since it is a right-angled triangle, it has base, perpendicular and hypotenuse.
Base = r
Perpendicular = 14
Hypotenuse = r + 7
<u>Using Pythagoras theorem:</u>
Put the values
(r + 7)² = (r)² + (14)²
Using formula a² + 2ab + b² = (a + b)²
r² + 14r + 49 = r² + 196
<em>Subtract</em> r² to both sides
14r + 49 = 196
<em>Subtract</em> 49 to both sides
14r = 196 - 49
14r = 147
<em>Divide</em> 14 to both sides
r = 147 / 14
r = 10.5
This is a problem of projectile motion. A projectile is an object you throw with an initial velocity and whose trajectory is determined by the effect of gravitational acceleration. The general equation in this case is described as:
Where:
So:
Finally, the equation is:
The rocket will reach the maximum height at the vertex of the parabola described by the equation . Therefore, our goal is to find
at this point. In math, a parabola is described by the quadratic function:
So the x-coordinate of the vertex can be calculated as:
From our equation:
So:
So the rocket will take its maximum value after 1.99 seconds.
<h2>c. What is the maximum height the rocket will reach?</h2>
From the previous solution, we know that after 1.99 seconds, the rocket will reach its maximum, so it is obvious that the maximum height is given by . Thus, we can find this as follows:
So the maximum height the rocket will reach is 66.68ft
<h2>d. How long is the rocket in the air?</h2>
The rocket is in the air until it hits the ground. This can be found setting , so:
We can't have negative value of time, so the only correct option is and rounding to the nearest hundredth we have definitively: