A pebble is dropped from rest from the top of a tall cliff and falls 4.9meters after 1 second has elapsed. How much further does it drop in the next 2 seconds?
To find the distance the pebble will drop in the next 2 seconds, we can make use of the equation of motion for a freely falling object. The equation is as follows:
d = (1/2) * g * t^2
Where:
d is the distance
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time
In this case, the pebble fell 4.9 meters in 1 second, so we can use this information to find the distance it will fall in the next 2 seconds.
First, let's calculate the distance fallen in 1 second using the equation. We'll plug in the values:
d = (1/2) * 9.8 * 1^2
d = 4.9 meters
Now, we can find the distance fallen in the next 2 seconds. We'll use the same equation, but with a time of 2 seconds:
d = (1/2) * 9.8 * 2^2
d = (1/2) * 9.8 * 4
d = 19.6 meters
Therefore, the pebble will drop an additional 19.6 meters in the next 2 seconds.
To find out how much further the pebble drops in the next 2 seconds, we need to calculate the total distance it covers in these 2 seconds.
The distance covered by an object falling under gravity is given by the formula:
d = (1/2) * g * t^2
where:
d is the distance traveled
g is the acceleration due to gravity (9.8 m/s^2 on Earth)
t is the time elapsed
Given that the pebble has already dropped 4.9 meters in the first second, we can calculate the additional distance it covers in the next 2 seconds.
For the first second:
d1 = (1/2) * 9.8 * 1^2
d1 = 4.9 meters
For the next 2 seconds:
d2 = (1/2) * 9.8 * 2^2
d2 = 19.6 meters
Therefore, the pebble will drop an additional 19.6 meters in the next 2 seconds.
d = (1/2) g t^2 = 4.9 t^2
at t = 0, d = 0
at t = 1, d = 4.9
at t = 2, d = 4.9*4
at t = 3, d = 4.9 * 9
so from t = 1 to t = 3
it falls
4.9 (9-1) = 4.9*5