Solving Uni Physics with Projectile Motion

[Stephen1993]

uni physics!

Homework Statement

A child runs down a 12 degrees hill and then suddenly jumps upward at a 15 degree angle above horizontal and land 1.4m down the hill as measured along the hill. What was the child's initial speed?

firstly, when he runs downhill with a certain velocity then how is that part of the component of velocity in the projectile motion? i am confused because the person jumps and so i wonder what happens to the velocity that the person has when he travels downhill
a diagram might help to explain things of what is happening like how the velocity that the boy runs downhill contribute to the velocity of the projectile motion.

thank you

 

[gneill]

Consider t = 0 to be when the child jumps and concentrate on the required trajectory from that moment. What "launch" velocity is required, with a 15° launch angle, to land 1.4m downslope?

 

[Stephen1993]

the trouble is how is the velocity that the person runs downhill related to the projectile motion?
because he jumps which means that he exert a force which makes him undergo projectile motion

ty

 

[gneill]

the trouble is how is the velocity that the person runs downhill related to the projectile motion?
because he jumps which means that he exert a force which makes him undergo projectile motion

Once you've got the launch velocity you can always break it down into components parallel to and normal to the slope, and assume that the action of the jump is to add the normal component to the initial downslope one.

 

[rwisz]

for the question and the diagram provided. It is important to understand that in projectile motion, the initial velocity is the combination of both the horizontal and vertical components. In this case, the child's initial velocity when he jumps is composed of the velocity he had when running downhill and the additional velocity he gained when jumping upwards.

To solve this problem, we can use the equations of motion for projectile motion. Firstly, we can use the equation for the horizontal displacement to find the horizontal component of the initial velocity. This will be equal to the distance traveled down the hill, which is 1.4m.

Next, we can use the equation for the vertical displacement to find the vertical component of the initial velocity. This will be equal to the height the child jumped, which can be calculated using trigonometry and the given angle of 15 degrees.

Once we have both the horizontal and vertical components of the initial velocity, we can use the Pythagorean theorem to find the magnitude of the initial velocity. This will give us the speed at which the child was running downhill before jumping.

In summary, the child's initial velocity is composed of both the horizontal and vertical components, and we can use the equations of motion for projectile motion to solve for the initial speed. I hope this helps clarify any confusion. Keep up the good work in uni physics!