A man drives his motorcycle horizontally off the end of a cliff and lands in the water 2 s later. How high is the cliff?
Question
A man drives his motorcycle horizontally off the end of a cliff and lands in the water 2 s later. How high is the cliff?
Solution
Sure, to solve this problem, we need to use the formula for the distance travelled under constant acceleration, which in this case is due to gravity. The formula is:
d = v_it + 0.5a*t^2
where:
- d is the distance travelled (which is the height of the cliff in this case),
- v_i is the initial velocity (which is 0 in this case because the man is falling straight down),
- a is the acceleration (which is the acceleration due to gravity, approximately 9.8 m/s^2), and
- t is the time (which is 2 seconds in this case).
Substituting the known values into the formula, we get:
d = 02 + 0.59.8*2^2
Solving this equation gives:
d = 0 + 0.59.84 = 19.6 meters
So, the cliff is approximately 19.6 meters high.
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