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Motion Problems

 

Motion problems are problems involving movement. Here is an example of a motion problem and solutions with steps. 

 

QUESTION:

 A football is punted into the air. Its height h, in metres, after t seconds is given by the equation h = −4.9t2 + 24.5t +1. 

  • a)  How high is the ball after 1 second? 

  • b)  Find the maximum height of the ball to one decimal place. 

  • c)  When does the ball reach its maximum height? 

  • d)  When does the ball hit the ground? 

a) How high is the ball after 1 second?

When the question asks the height of the ball after any number of seconds, just plug i the time in the equation and solve for height.

b)  Find the maximum height of the ball to one decimal place. 

When the question asks for maximum height, it means to find the y value of the vertex because in this case it is the highest point on the parabola. 

c)  When does the ball reach its maximum height? 

 

When the question asks about when the maximum height is achieved, it means to find the x value of the vertex. In these many seconds, the ball will be the highest.

d)  When does the ball hit the ground? 

When the question asks the amount of time it takes for the ball to hit the ground, we have to find the x-intercepts of the parabola. Since time cannot be negative, we have to choose to positive x-intercept which displays how much time it took for the ball to come at a stop.

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