A boy having a weight of 90 lb lb jumps off a wagon with a...

A boy, having a weight of 90 lb lb, jumps off a wagon with a relative velocity of vb/w=6 ft/svb/w=6 ft/s. If the angle of jump is 30∘30∘, determine the horizontal velocity (vw)2(vw)2 of the wagon just after the jump. Originally both the wagon and the boy are at rest. Also, compute the total average impulsive force that all four wheels of the wagon exert on the ground if the boy jumps off in Δ t=0.8 sΔ t=0.8 s. The wagon has a weight of 20 lb lb.

Transcript

00:01 Hello, in this question we are given that there are two wagons and a dog.

00:05 Okay, dog jumps from wagon a to wagon b and his velocity is just a second.

00:16 It is five feet per second at an angle of 5 12 13 triangle.

00:23 So its initial speed with respect to most of the dog with respect to one is.

00:31 This is given to us that is five and this angle 3.

00:35 Is we can calculate this angle theta using this triangle 5 12 13 and this is the angle theta so 10 inverse 5 by 12 is the angle theta so we can calculate this value let me calculate the value of theta first so further we will solve it 10 inverse 5 by 12 so it is 22 .62 degree so the dog is jumping at an angle of this so so as we know that velocity of dog with respect to ground will be, velocity of dog with respect to 1 plus velocity of 1 with respect to ground.

01:19 All right.

01:20 And assuming backward direction as positive in case of first jump.

01:28 Okay.

01:29 So forward direction would be, sorry, it would be negative then.

01:34 Right.

01:35 So conserving linear momentum in first case in horizontal direction.

01:39 What do we get? initially, they both are at rest.

01:44 So, initial momentum would be zero.

01:46 Then final momentum would be momentum of dog in horizontal direction would be what mass of the dog into velocity of dog in horizontal? so it would be mass of the dog into velocity of dog in horizontal with respect to what? ground minus, because wagon will move in the rightward direction.

02:13 I am assuming that wagon is moving in the rightward direction with this much velocity.

02:17 So it would be ultimately negative.

02:20 So it would be minus of mass of 1 into velocity of 1 with respect to ground.

02:28 Also over here it will come out to be negative because if this is the wagon and this is the dog, it moves with a velocity of v of dog with respect to 1 and this itself moves in the right word direction with velocity of 1 with respect to ground so velocity of dog with respect to ground would be nothing but velocity of d with respect to 1 plus velocity of 1 with respect to round but over here the direction of v is right words so this sign would change to negative so you can clearly see the that velocity of the dog with respect to ground would be nothing but mass of the dog is 90 pounds into velocity of the dog with respect to ground would be 5 cos theta 5 times cost 22 .62 degrees minus low speed of the one with respect to ground minus what was it it was weight of the so weight of the dog is 55 and wagon is 90 this is 55 this is 55 this is 55 and this is 55 and this over here is 90 into v1.

03:53 So from here we can calculate value of v1 with respect to ground.

03:56 So it will be coming out to be let me calculate the value 5 into 55 into cost 22 .62 divided by 90 plus 55.

04:14 So this will be coming out to 1 .751 feet per second.

04:20 So this is velocity of the wagon 1.

04:24 And horizontal velocity of the dog would be, velocity of dog with respect to ground would be nothing but vd1 that was 5 cost 22 .62 minus 1 .751...

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