### Rock Thrown Off Cliff - Problem AnalysisA rock is thrown off of a 100-foot cliff with an upward velocity of 50 m/s. As a result, its height after \( t \) seconds is given by the formula:\[ h(t) = 100 + 50t - 5t^2 \]We are tasked with determining the following:1. **What is its height after 3 seconds?** \[\boxed{} \]2. **What is its velocity after 3 seconds?** \[\boxed{} \]*(Positive velocity means it is on the way up, negative velocity means it is on the way down.)*### Detailed Explanation#### Calculating Height After 3 SecondsTo find the height of the rock after 3 seconds, substitute \( t = 3 \) into the height function \( h(t) \):\[ h(3) = 100 + 50(3) - 5(3)^2 \]Simplify the expression to determine the rock's height after 3 seconds.#### Calculating Velocity After 3 SecondsThe velocity \( v(t) \) of the rock can be found by differentiating the height function \( h(t) \):\[ v(t) = \frac{dh(t)}{dt} \]\[ v(t) = \frac{d}{dt}\left(100 + 50t - 5t^2\right) \]\[ v(t) = 50 - 10t \]To find the velocity after 3 seconds, substitute \( t = 3 \) into the velocity function:\[ v(3) = 50 - 10(3) \]Simplify the expression to determine the rock's velocity after 3 seconds.For further practice, you can manipulate the equations to see how different initial velocities and heights impact the results.

A rock is thrown off of a foot cliff with an upward velocity of . As a result its height after…

A rock is thrown off of a 100 foot cliff with an upward velocity of 50 m/s. As a result its height after t seconds is given by the formula: h(t) = 100+50t - 5t² What is its height after 3 seconds? What is its velocity after 3 seconds? 9 (Positive velocity means it is on the way up, negative velocity means it is on the way down.)