Please help with these two projectile motion problems, thanks

In summary, the first conversation involves finding the object's vertical displacement at a given time and angle of trajectory. The second conversation involves finding the maximum vertical displacement for two different launch angles and calculating the difference between them.
  • #1
shaunamariexx
2
0
#1:

Homework Statement


A projectile is launched at an angle of 64.9 degrees with the horizontal (x axis) at some unknown velocity. After 4.6 seconds, the object's angle of trajectory is 40.3 degrees above the horizontal. What is the object's vertical displacement at this time in meters? (Hint: first find the magnitude of the initial velocity using the angle of trajectory (draw a triangle and relate components) and the equation for the final velocity in the y direction.The attempt at a solution
I first tried to find the magnitude of the initial velocity using the trajectory but I had some trouble! And then I know there is an equation for the final velocity in the y direction to help with the answer.

#2:

Homework Statement
A projectile is lauched at some speed at an angle of 62 degrees and travels a range of 220 meters. The launch angle is then changed, but the projectile is fired at the same speed as the original case and also travels the same range of 220 meters. Find the maximum vertical displacement at 62 degrees, (ymax1), and find the maximum vertical displacement for the second angle (ymax2), and then find the difference between them in meters

The attempt at a solution
I know after I find the ymax values to subtract ymax2 from ymax 1
 
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  • #2
shaunamariexx said:
A projectile is launched at an angle of 64.9 degrees with the horizontal (x axis) at some unknown velocity. After 4.6 seconds, the object's angle of trajectory is 40.3 degrees above the horizontal. What is the object's vertical displacement at this time in meters? (Hint: first find the magnitude of the initial velocity using the angle of trajectory (draw a triangle and relate components) and the equation for the final velocity in the y direction.
Let uy= initial vertical component of velocity and vy=final vertical velocity.
Horizontal component of velocity i.e. vx is same throughout the journey.
tan(64.9°)=uy/vx
tan(40.3°)=vy/vx
Taking ratio,
uy/vy=2.5172
uy=2.5172vy-------(1)
Also,
vy=uy-gt
From 1,
vy=2.5172vy-gt
∴1.5172vy=gt
∴vy=gt/1.5172
vy=29.74m/s
uy=74.86m/s
Also, vertical displacement
s=(uy2-vy2)/2g
s=240.80m
 
  • #3
shaunamariexx said:
A projectile is lauched at some speed at an angle of 62 degrees and travels a range of 220 meters. The launch angle is then changed, but the projectile is fired at the same speed as the original case and also travels the same range of 220 meters. Find the maximum vertical displacement at 62 degrees, (ymax1), and find the maximum vertical displacement for the second angle (ymax2), and then find the difference between them in meters
For having the same range, the angles should be complementary i.e. θ1+θ2=90°.
(Because R=v2sin(2θ)/g
and if θ1+θ2=90°, sin(2θ1)=sin(2θ2)).
So, the other angle of projection is 28°.
Rest of the calculations are pretty straightforward.
 

1. What is projectile motion?

Projectile motion is the motion of an object through the air that is subject to gravity and air resistance. It follows a curved path called a parabola.

2. How do I solve projectile motion problems?

To solve a projectile motion problem, you need to break it down into horizontal and vertical components. You can use equations of motion and the principles of trigonometry to solve for the initial velocity, time of flight, and maximum height or range of the projectile.

3. What are the key factors that affect projectile motion?

The key factors that affect projectile motion are initial velocity, angle of launch, air resistance, and gravity. The initial velocity and angle of launch determine the initial velocity components, while air resistance and gravity affect the acceleration of the object.

4. 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 the range, you can use the equation: range = (initial velocity * cos(angle of launch)) * (initial velocity * sin(angle of launch))/gravity.

5. Can you explain the difference between horizontal and vertical motion in projectile motion?

In projectile motion, horizontal motion refers to the motion of the object in the x-direction, while vertical motion refers to the motion in the y-direction. Horizontal motion is constant, while vertical motion is affected by gravity. Together, they determine the path of the projectile.

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