The goal is to shoot down my friends drone with a paintball. We need to know how quickly my paintball will reach a maximum altitude. And we need to know if my paintball will even reach the height required to reach the drone. His drones maximum altitude is 1200 ft.

A paintball will be shot directly upward with an initial velocity of 293 feet per second (approximately 200 mph) from an initial height of 7 ft. The height of the paintball (in feet) after t seconds if given by formula h(t)=-16t2+293t+7. After how many second will the ball reach its maximum height? What is that maximum height?

How many seconds will the Paintball take to reach maximum altitude. (Round to the nearest whole number)

What is the maximum altitude of the paintball? (Round to the nearest whole number)

Thanks!

So we need the vertex of the parabola

h(t) = -16t^2 + 293t + 7
the t of the vertex is -b/(2a) = -293/-32 = 293/32 seconds or in 9.15625 seconds

plug that into h(t)
= ...
= appr 1348.4 ft

your next two questions have just been answered

To find the time it takes for the paintball to reach its maximum height, we can use the formula for the vertex of a quadratic equation. The quadratic equation that represents the height of the paintball is h(t) = -16t^2 + 293t + 7, where h(t) is the height at time t.

The formula for finding the time it takes to reach the maximum height is given by t = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0. In this case, a = -16 and b = 293.

So, substituting the values into the formula, we get t = -293 / (2 * -16).

Calculating this, we find t ≈ 9.15625 seconds. Rounded to the nearest whole number, the paintball will take approximately 9 seconds to reach its maximum height.

To find the maximum height of the paintball, we can substitute the value of t we just found into the equation h(t) = -16t^2 + 293t + 7.

Using t = 9, we have h(9) = -16(9)^2 + 293(9) + 7.

Evaluating this expression, we find h(9) ≈ 1960. Rounded to the nearest whole number, the maximum altitude the paintball reaches is approximately 1960 feet.

So, the answers to your questions are:

The paintball will take approximately 9 seconds to reach its maximum height.

The maximum altitude the paintball reaches is approximately 1960 feet.