A person wearing a seatbelt has a good chance of surviving a car crash if the magnitude of the deceleration is no more than 300 m/s2. Over what duration must a crash occur for the occupants of the car to survive being brought to a standstill from an initial speed of 100km/hr?
A froghopper is a small insect which can launch itself upwards with an acceleration of about 400 times gravity. In the first stage of its jump, while its feet are in contact with the ground, the froghopper accelerates to reach a top speed of 4.0m/s. This is reached when its body is 2mm above the ground. After losing contact with the ground, acceleration is then only due to gravity. Calculate the following (ignoring air resistance):
(a) The time to reach a maximum height
(b) The maximum height reached
(c) The speed on hitting the ground
0.09 seconds
To determine the duration of the crash, we can use the formula for deceleration:
a = (vf - vi) / t
Where:
a = deceleration (in m/s^2)
vf = final velocity (in m/s)
vi = initial velocity (in m/s)
t = time (in seconds)
We are given the following information:
a = 300 m/s^2
vi = 100 km/hr = 27.8 m/s (since 1 km/hr is equal to 0.278 m/s)
We need to find the duration of the crash (t) required for the occupants to survive.
Given that the final velocity (vf) is 0 m/s (since the car will be brought to a standstill), we can rearrange the formula to solve for time (t):
t = (vf - vi) / a
Substituting the known values into the equation:
t = (0 - 27.8 m/s) / 300 m/s^2
Simplifying the equation, we get:
t = -27.8 / 300
Now, let's calculate the value of t:
t ≈ -0.0927 seconds
Since time cannot be negative in this context, we take the absolute value:
t ≈ 0.0927 seconds
Therefore, the crash must occur over at least 0.0927 seconds for the occupants of the car to survive being brought to a standstill from an initial speed of 100 km/hr.