an object is dropped from a vertical cliff. How long does it take to reach 85 km/h?
v = at
where a is just the acceleration due to gravity. So, solve for t in
9.8t = 85(1000/3600)
To find out how long it takes for an object to reach a speed of 85 km/h when dropped from a vertical cliff, we need to consider the motion of the object.
The motion of a falling object can be described using the equations of motion. In this case, we can use the equation:
v = u + at
Where:
v is the final velocity of the object (85 km/h),
u is the initial velocity of the object (0 km/h as it is dropped),
a is the acceleration due to gravity (-9.8 m/s^2 for objects falling near the Earth's surface), and
t is the time taken for the object to reach the final velocity.
First, we need to convert the speed from km/h to m/s as the equation uses meters per second. We know that 1 km/h is equal to 0.2778 m/s. Therefore, 85 km/h is equal to:
85 km/h * 0.2778 m/s = 23.61 m/s
Now we can substitute the values into the equation:
23.61 m/s = 0 m/s + (-9.8 m/s^2) * t
Simplifying the equation, we have:
23.61 m/s = -9.8 m/s^2 * t
Dividing both sides of the equation by -9.8 m/s^2, we find:
t = 23.61 m/s / -9.8 m/s^2
t ≈ -2.41 seconds
Since time cannot be negative, we discard the negative sign, and thus the object takes approximately 2.41 seconds to reach a speed of 85 km/h when dropped from the vertical cliff.
Note: This calculation assumes no air resistance. In real-world scenarios, air resistance can affect the time it takes for the object to reach a certain speed, but for simplicity, we have ignored it in this explanation.