Question

100 POINTS

final part/questions so i can complete my written math assignments

Task 2: Height of a Projectile
The height of a projectile that has been launched upward can be determined by finding the sum of the product of one-half of the object’s acceleration and t2, the product of the object’s initial velocity and t, and the object’s initial height, where t represents the number of seconds after the object has been launched. An object’s acceleration can be assumed to be -32 ft/s2, which is the acceleration due to gravity.

A. Why do you think the acceleration due to gravity is represented by a negative number?

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B.Write a formula to represent the height of a projectile for any given time t.

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C.If a projectile is launched into the air from the ground with an initial velocity of 192 feet per second, how long after launch will the projectile be at a height of 320 feet? Show your work.

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D. Can you use your previous answer to determine how long it will take for the object to reach its maximum height? If so, determine how long it will take and find the maximum height.

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E.How long after launch will the projectile land on the ground? Show your work.

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F. If the initial velocity stays the same, but the height the projectile is launched from changes, how would the amount of time it takes for the projectile to reach its maximum height change? How would its maximum height change?

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G. Assuming the velocity stays the same, at what height above the ground does the projectile need to be launched to increase the amount of time it will take for the projectile to return to the ground by one second?

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Answer 1

A. The acceleration due to gravity is represented by a negative number because it acts in the opposite direction of the upward motion of the projectile. It pulls the object downward, causing it to decelerate and eventually fall back to the ground.

B. The formula to represent the height of a projectile at any given time t is: h = (0.5 * a * t^2) + (v * t) + h0, where h is the height, a is the acceleration (-32 ft/s^2), t is the time, v is the initial velocity, and h0 is the initial height.

C. To find the time when the projectile is at a height of 320 feet, we can set h = 320 in the formula and solve for t. 320 = (0.5 * -32 * t^2) + (192 * t) + 0. Solve the quadratic equation to find the value of t.

D. To find the time it takes for the object to reach its maximum height, we need to find the time when the velocity becomes zero. Set v = 0 in the formula and solve for t. Then substitute the value of t into the formula to find the maximum height.

E. To find the time when the projectile lands on the ground, we need to find the time when the height becomes zero. Set h = 0 in the formula and solve for t.

F. If the initial velocity stays the same but the height the projectile is launched from changes, the amount of time it takes for the projectile to reach its maximum height will remain the same. However, the maximum height will change based on the initial height.

G. To increase the amount of time it takes for the projectile to return to the ground by one second, we need to find the height that corresponds to that additional time. Set the time to (t + 1) in the formula and solve for h. Subtract the initial height from the result to find the height above the ground from which the projectile needs to be launched.

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~~~Harsha~~~