Applied Calculus – We throw a ball upwards

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) = –t² +50t+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) = –t² +50t+1

h = -0² +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.