An arrow is shot from a height of 16 m toward a cliff of...

An arrow is shot from a height of 1.6 m toward a cliff of height H. It is shot with a velocity of 26 m/s at an angle of 60° above the horizontal. It lands on the top edge of the cliff 3.8 s later. A, What is the height of the cliff (in m)? B. What is the maximum height (in m) reached by the arrow along its trajectory? C. What is the arrow's impact speed (in m/s) just before hitting the cliff?

Transcript

00:01 We are given that an arrow is shot from a height of 1 .6 meter at an angle of theta equal to 60 degree with initial speed u equal to 26 meter per second and here we have a cliff of height capital h and we are given that the arrow lands on top of clip after t equal to t equal to 3 .8 second arrow lands on top of clip.

00:31 On top of cliff now in the first part of the cushion we are going to find the total height of the clip so for in the first part so in order to find the total height first we are going to find this small edge so for this projectile motion the value of small edge is going to be u sine theta multiply t minus 1 by 2 gt square now put the values 26 multiply sign 60 degree minus 1 by 2 multiply 9 .8 multiply 3 .8 and it's a square so it comes out to be around 14 .8 meter now we are going to find the height of clip so h will be equal to small h plus 1 .6 meter that is 14 .8 plus 1 .6 it comes out to be 16 .4 meter this is the height of the clip now in the b part of the question the we are going to find the maximum height reached by arrow maximum height reached by arrow so that h maximum maximum that will be equal to u square sine square theta by 2g that is in the projectile motion so we can write it as 26 multiply 26 multiply sine square 60 degree divide 2 multiply 9 .8 now if you solve this then we get 25 .86 meter and the maximum height from ground maximum height from ground that will be equal to 1 .6 plus 25 .86 it comes out to be 27 .46 now in the c part of the cushion 27 .46 meter now in the c part of the cushion we are going to find the velocity of the arrow just before it hits the cliff so arrow impact arrow impact speed on cliff just before it hits the top just before it hits the top so, v will be equal to under root vx square plus vy square.

03:15 It will comprises of two components, horizontal and vertical...

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