Word problem: initial height of projectile

[mathdrama]

A ball is thrown from a cliff. The path of the ball modeled by the equation
h = -5t^2+ 5t + 210,
where h is the height, in metres, of the ball above the ground, and t is the time, in seconds, after it is thrown. How high is the cliff?

Not really sure how to do this problem. I know that one of the roots is -6, but I don't know how to use this information.

 

[mathmari]

Re: word problem

A ball is thrown from a cliff. The path of the ball modeled by the equation
h = -5t^2+ 5t + 210,
where h is the height, in metres, of the ball above the ground, and t is the time, in seconds, after it is thrown. How high is the cliff?

Not really sure how to do this problem. I know that one of the roots is -6, but I don't know how to use this information.

Since $t$ is the time after the ball is thrown, you have to set $t=0$ at the equation to find the height of the ball before it's thrown, so when it is still on the cliff.

 

[mathdrama]

Re: word problem

So to make sure I have this right...

Let t = 0
h = -5(0^2) + 5(0) + 210
h = 0 + 0 + 210
h = 210
Therefore, the cliff is 210 meters high.

 

[mathmari]

Re: word problem

So to make sure I have this right...

Let t = 0
h = -5(0^2) + 5(0) + 210
h = 0 + 0 + 210
h = 210
Therefore, the cliff is 210 meters high.

Yes, it is right! (Yes)

 

[CellCoree]

I would approach this problem by first understanding the given equation and its components. The equation models the height of the ball, h, in relation to time, t, after it is thrown. The -5t^2 term indicates that the ball is experiencing a downward acceleration due to gravity, while the +5t term represents the initial velocity of the ball. The constant term, 210, represents the initial height of the ball.

To find the initial height of the cliff, we need to find the value of h when t is equal to 0, as this would represent the height of the ball at the moment it is thrown. Substituting t=0 into the equation, we get:

h = -5(0)^2 + 5(0) + 210 = 210

This means that the initial height of the ball, and therefore the height of the cliff, is 210 meters.

To further verify this result, we can also use the fact that one of the roots of the equation is -6. This means that at t=-6, the ball will reach the ground and h will be equal to 0. Substituting t=-6 into the equation, we get:

h = -5(-6)^2 + 5(-6) + 210 = 0

This confirms that the initial height of the cliff is 210 meters, as the ball reaches the ground after 6 seconds.

In summary, the initial height of the cliff can be found by substituting t=0 into the given equation, and the result is 210 meters. Alternatively, we can use the fact that one of the roots of the equation is -6 to verify this result.