## Description

We throw a ball upwards – This document contains the worked out solutions to the following questions:

We throw a ball upwards. Its height *h* (in meters), *t* seconds after its launch is given by the following equation

*h*(*t*) = –*t*^{2} +50*t*+1

- Find the initial height of the ball.
**Round your answer to 4 decimals if needed and show your calculations. Use the correct notation.** - Find at what time the speed of the ball is zero and find the height of the ball at this moment.
**Round your answer to 4 decimals if needed and show your calculations. Use the correct notation.** - Use the derivative to find the speed of the ball precisely when it will touch the ground after its launch.
**Round your answer to 4 decimals if needed and show your calculations. Use the correct notation.** - Calculate the speed and the acceleration of the ball 3 seconds after its launch.
**Round your answer to 4 decimals if needed and show your calculations. Use the correct notation. Here is a preview of the document.** - Interpret the results of c in the context of the problem. You must write an interpretation ….

**Solutions**

- Find the initial height of the ball.
**Round your answer to 4 decimals if needed and show your calculations.**

**a) Initial height of the ball**

Initial height is when time t = 0

*h*(*t*) = –*t*^{2} +50*t*+1

*h* = -0^{2} +50 x 0+1 = 1

*h* = 1 meter

**b) Time at which speed of the ball is zero, and height of the ball at this moment. Round your answer to 4 decimals if needed and show your calculations.**

Speed s = …..

Solutions: t = 25 seconds, *h* = 626 meters

Find all worked out (well explained) solutions to the above questions.

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