Question

The number of seconds, t it takes for an object to fall a distance of d meters can be found using the formula t=2dg‾‾‾√, where g is the constant acceleration due to gravity, 9.8 m/sec2. how many meters does an object fall in 4 seconds? round your answer to the nearest whole number.

Answer 1

S = V0 t + 1/2 g t^2 formula for distance traveled by accelerating object

Since V0 = 0

S = 1/2 g t^2

Can be written t = (2 S / g)^1/2

S = 1/2 * 9.8 * 4^2 = 78.4 m

An object will fall 78.4 m in the first 4 seconds

Answer 2

To find the distance an object falls in 4 seconds given the gravity constant, we rearrange the formula, substitute the values, and calculate, resulting in a distance of 78 meters when rounded to the nearest whole number.

Step-by-step explanation:

To find the distance d that an object falls in 4 seconds, we can rearrange the given formula t = √(2d/g), where t is time in seconds, d is distance in meters, and g is the acceleration due to gravity, which is 9.8 m/s2. Squaring both sides of the equation, we get t2 = 2d/g, and then multiply both sides by g to isolate d, giving us d = gt2/2. Plugging in the values, d = (9.8 m/s2)(4 s)2/2. Simplifying, d = (9.8 m/s2)(16 s2)/2 = 78.4 m. Rounding to the nearest whole number, the object falls 78 meters in 4 seconds.