Really boring day
Heathcliff was standing at the top of a building. Katherine was on the top of a building across the street that was 120 meters higher than Heathcliff's. They each had a vast collection of tennis balls. In order to alleviate their boredom, they decided to play a game. Each time Heathcliff dropped a ball, Katherine threw her ball toward the ground. They decided to continue this little game -to the chagrin of pedestrians-until their balls reached the ground at the same time. Each time Katherine threw her ball down at a different speed. Her ball finally hit the ground at the same time as Heathcliff's when she threw her ball at 15 meters per second. The question is: how high was Heathcliff's building (in meters)? (Assume g = 10 m/s; neglect air resistance and the fact that Heathcliff and Katherine are fictional characters I stole to use in this silly problem.)
The answer is 320.
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1 solution
Let the height be 'h'.
Therefore Katherine's building's height is 120+h.
By the problem,
h=1/2 x10 x t 2
h=5 t 2 ............................. i
again,
h + 120 =15t + 1/2 x10 x t 2
or, h + 120 =15t + h(inserting value of i) or, t=8
Therefore, h= 320m