A calculate the height in m of a cliff if it takes 24 s for...

a) Calculate the height (in m) of a cliff if it takes 2.4 s for a rock to hit the ground when it is thrown straight up from the top of the cliff with an initial velocity of 6 m/s. b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed?

Transcript

00:01 Hello and welcome to this video solution of numerate.

00:04 So here you have to calculate the height of a cliff if it takes a time of 2 .4 seconds to hit the ground when it is thrown straight up from the top of a clip with initial speed of 6 meters per second, right? this height, let's say as you have to calculate and the initial speed is upward which is equal to 6 meters per second, right? and that total time of to hit the ground is 2 .4 right now this is pretty simple so what you can apply is a net displacement is s which is equal to u t plus half a t squared right now this displacement will be in the downward direction right so it's negative of the okay so you have to calculate it right so yes you have to calculate yes u is directed upwards so it's six times of time is 2 .4 plus half now the acceleration is acting downright this is g which is minus 9 .8 in this case right because you have considered u as 6 which is in the upward direction as positive now the g you have to consider negative this sum sign is pretty important right and time is 2 .4 squared so let's see how much we're getting it's 13 .8 minus 13 .8 meters right so the height is 13 .8 right magnitude is you have to consider only the magnitude which is 13 .8 meters you can write next how long it will take to reach the ground if it's thrown straight down with the same speed right again you have to apply s equal to u t plus half 80 square right now this is you can consider the downward direction as positive now no okay so it's 13 .8 is a positive downward it's moving down right u is also down now 6 t you have to calculate plus half here we have 9 .8 and t squared so everything is acting downwards right so let me just draw it downward direction is considered positive in this case 4 .9 t squared plus 60 minus 13 .8 equal to 0 so this is a quadratic equation and let's evaluate and see how much we're getting for t it's 1 .17 seconds right the other value of t is negative so we will neglect it so this is the time it will take to reach the ground...

Question

a) Calculate the height (in m) of a cliff if it takes 2.4 s for a rock to hit the ground when it is thrown straight up from the top of the cliff with an initial velocity of 6 m/s. b) How long (in s) would it take to reach the ground if it is thrown straight down with the same speed?

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