Problem 1 Ha-Joon (d) clays tennis throws a boll straight up into the air from the ground with an initial velocity of 2 meters per second during a surt. The height of the ball at any time t (in seconds) is given by the equation: h(t)=-t^2+2t+1.5 where (t) is the height of the tennis ball in meters. Questions: 1. How long will it take for the tennis ball to reach its maximum height? 2. What is the maximum height the tennis ball will reach? 3. Assuming Ha-loon (9) does not to hit the tennis ball during the surf, after how many seconds will the tennis ball hit the ground? (Round to the nearest 10^m second.)

Question

Problem 1 Ha-Joon (d) clays tennis throws a boll straight up into the air from the ground with an initial velocity of 2 meters per second during a surt. The height of the ball at any time t (in seconds) is given by the equation: h(t)=-t^2+2t+1.5 where (t) is the height of the tennis ball in meters. Questions: 1. How long will it take for the tennis ball to reach its maximum height? 2. What is the maximum height the tennis ball will reach? 3. Assuming Ha-loon (9) does not to hit the tennis ball during the surf, after how many seconds will the tennis ball hit the ground? (Round to the nearest 10^m second.)

Answer 1

1. To find the time it takes for the tennis ball to reach its maximum height, we need to find the time at which the velocity of the ball is zero. The velocity of the ball is the derivative of the height function with respect to time. So, we need to find the derivative of the height function and set it equal to zero.The height function is given by:

Taking the derivative, we get:

Setting the derivative equal to zero, we get:

So, it will take 1 second for the tennis ball to reach its maximum height.2. To find the maximum height the tennis ball will reach, we need to substitute the time at which the ball reaches its maximum height (which we found in the previous step) into the height function.Substituting

into the height function, we get:

So, the maximum height the tennis ball will reach is 2.5 meters.3. To find the time at which the tennis ball will hit the ground, we need to find the time at which the height of the ball is zero. So, we need to set the height function equal to zero and solve for

.Setting the height function equal to zero, we get:

This is a quadratic equation, which can be solved using the quadratic formula:

In this case,

,

, and

. Plugging these values into the quadratic formula, we get:

Simplifying further, we get:

Since time cannot be negative, we take the positive root:

Using a calculator, we find that

, so:

Rounding to the nearest tenth of a second, we get:

secondsSo, the tennis ball will hit the ground after approximately 2.6 seconds.

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