Question
A ball is thrown into the air from the top of a cliff. The
height,
, of the ball above the ground
seconds after
it is thrown can be modeled by the following function.
How many seconds after being thrown will the ball hit the ground?
height,
it is thrown can be modeled by the following function.
How many seconds after being thrown will the ball hit the ground?
Ask by Harper Fowler. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The ball will hit the ground after 6 seconds.
Solution

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Extra Insights
To find out when the ball hits the ground, we need to determine when the height
is equal to zero. We can set the equation
and solve for
using the quadratic formula, where
,
, and
. The formula is given by
. Plugging in the values, we find the two possible solutions for
. Generally, one is negative and doesn’t apply here, while the positive solution represents the time when the ball reaches the ground.
We can simplify the calculation; by determining the
part first:
.
Now applying the quadratic formula gives us real-world insights into projectile motion commonly seen in sports, entertainment, and physics.
Now applying the quadratic formula gives us real-world insights into projectile motion commonly seen in sports, entertainment, and physics.
This formula is commonly used in physics for solving problems related to projectile motion, allowing one to determine where an object will land after being launched. Remember, the height function can change based on variables like initial velocity, angle of launch, and environmental factors—so different scenarios could further engage your problem-solving skills and creativity in real life.