Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. write an equation and answer the questions below. show all your work for full credit. use the correct units with your answers

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.

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

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:

c

c

c

c

c

c

c

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c

step-by-step explanation:

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt