QuestionFind the time $t$ for a ball dropped from a 1515 m building using $d=\frac{1}{2}gt^2$ . Options: 18.10s, 17.12s, 17.75s, 17.58s.

Studdy Solution

STEP 1

Assumptions1. The height from which the ball is dropped is1515 meters. . The acceleration due to gravity (g) is9.8 m/s^.
3. The equation for distance travelled by an object under gravity is d = \frac{1}{}gt^.

STEP 2

We need to find the time (t) it takes for the ball to reach the ground. We can do this by rearranging the equation to solve for t.
$t = \sqrt{\frac{2d}{g}}$

STEP 3

Now, plug in the given values for the distance (d) and acceleration due to gravity (g) to calculate the time.
$t = \sqrt{\frac{2 \times1515}{9.8}}$

STEP 4

Calculate the time it takes for the ball to reach the ground.
$t = \sqrt{\frac{2 \times151}{9.8}} \approx17.58 \, seconds$ The ball takes approximately17.58 seconds to reach the ground. Therefore, the correct answer is17.58 seconds.

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