Kinematics with projectile motion(2 questions)

In summary, the conversation discusses the calculations needed for jumping a gorge on a skateboard and the required speed to safely make it to the other side. The answer is determined to be 23 m/s, with the formula 50 = (v2*sin(2*30))/9.81. For a different scenario with a ramp inclined at 45 degrees and a speed of 20 m/s, the person would not make it to the other side and would fall short by 9 to 10 meters, with the formula -1 = (20*sin45)t -4.91*t2.
  • #1

koolaid123

2
0
1) Jim decides to jump a gorge on his skateboard. The gorge is 50 m wide and jim has constructed a 1 m high ramp iclined at 30 degrees to the horizontal. If air resistance is neglected, calculate what speed Bart must reach if he is to land safely on the other side of the gorge.

The answer is 23 m/s but I don't know how to get it.

2) Jake has calculated that he can jump the jorge if the ramp is inclied to 45 degrees, and he attains a speed of 20 m/s. Will Jake make it? If not how much short of the other side is he when he drops below the level of the ground?

The answer is no, and 9 m but i don't know how to get it.
 
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  • #2
Looks like homework.

With v as initial velocity, can you calculate the horizontal and vertical component of the velocity?
Based on the vertical component, can you calculate the time until Jim/Bart is at floor level again?
Based on that time, can you calculate the horizontal position at that point?

That can be used for both 1 and 2.
 
  • #3
koolaid123 said:
1) Jim decides to jump a gorge on his skateboard. The gorge is 50 m wide and jim has constructed a 1 m high ramp iclined at 30 degrees to the horizontal. If air resistance is neglected, calculate what speed Bart must reach if he is to land safely on the other side of the gorge.

The answer is 23 m/s but I don't know how to get it.

2) Jake has calculated that he can jump the jorge if the ramp is inclied to 45 degrees, and he attains a speed of 20 m/s. Will Jake make it? If not how much short of the other side is he when he drops below the level of the ground?

The answer is no, and 9 m but i don't know how to get it.

1) Use this
50 = (v2*sin(2*30))/9.81
v=23.xx m/sec

2) Jake doesn't make it. Misses by 9m to 10m. You can use the same formula above but more accurate is
-1 = (20*sin45)t -4.91*t2
(-1, because the ramp is 1 m high). Solve for t. Use value of t in
x = (20*cos45)*t.
x will be much lower than 50m.

I think I'm right, but may be not.
 
  • #4
Neandethal00 said:
1) Use this
50 = (v2*sin(2*30))/9.81
v=23.xx m/sec
I think you forgot the height of the ramp here.
 
  • #5
mfb said:
I think you forgot the height of the ramp here.

Didn't forget, tried a quick-fix. ha ha
It gives the same answer OP was looking.
Thanks.
 

What is projectile motion?

Projectile motion is the motion of an object through the air. It is a type of motion that involves both horizontal and vertical components, where the object moves along a curved path due to the influence of gravity.

What is the difference between scalar and vector quantities in projectile motion?

Scalar quantities in projectile motion only have a magnitude, such as speed or distance. Vector quantities have both a magnitude and direction, such as velocity or displacement. In projectile motion, the horizontal component is a scalar quantity while the vertical component is a vector quantity.

How do you calculate the range of a projectile?

The range of a projectile is the horizontal distance it travels before hitting the ground. To calculate it, you can use the equation: range = (initial velocity)^2 * sin(2*angle of launch) / gravitational acceleration. This equation assumes no air resistance and a flat, horizontal surface.

What is the maximum height of a projectile?

The maximum height of a projectile is the highest point it reaches in its trajectory. To calculate it, you can use the equation: maximum height = (initial velocity)^2 * sin^2(angle of launch) / 2*gravitational acceleration. This equation also assumes no air resistance and a flat, horizontal surface.

How does air resistance affect projectile motion?

Air resistance can have a significant impact on projectile motion. It can decrease the range and maximum height of a projectile, as well as change its trajectory. Calculating the effects of air resistance on projectile motion can be complex and often requires advanced mathematical models and simulations.

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