A tiger leaps horizontally from a 5.7 m high rock with a speed of 3.9 m/s. How far from the base of the rock will she land?
time in air is the time it takes to fall 5.7m
time=sqrt (2*5.7/9.8) seconds
distance horizonta=3.9m/s* timetofall
To find out how far the tiger will land from the base of the rock, we can use the equations of motion. In this scenario, the vertical motion and horizontal motion are independent of each other.
First, let's calculate the time it takes for the tiger to reach the ground. We can use the equation:
h = (1/2) * g * t^2
Where:
h = height of the rock (5.7 m)
g = acceleration due to gravity (9.8 m/s^2)
t = time
Rearranging the equation, we get:
t^2 = (2 * h) / g
Substituting the given values, we have:
t^2 = (2 * 5.7) / 9.8
Now we can solve for t:
t = sqrt((2 * 5.7) / 9.8)
t ≈ 0.8801 s
Since the horizontal motion is not affected by gravity, the horizontal distance traveled can be calculated using the formula:
distance = speed * time
Substituting the given values:
distance = 3.9 m/s * 0.8801 s
distance ≈ 3.432 m
Therefore, the tiger will land approximately 3.432 meters away from the base of the rock.