Throwing Rocks: Analyzing Horizontal & Vertical Motion

In summary, a rock is thrown at an angle of 17 degrees above the horizontal at a speed of 28.5 m/s from the ground. To find the maximum height, the formula d=vit+1/2at^2 was used, resulting in a height of 37.87 m. The horizontal velocity remains constant at 28.5cos(17) m/s. To find the time when the rock reaches a vertical speed of zero, the equation y(t) = y_0 + (V_0)t-4.9t^2 was used, with the solution being 2.78 seconds. This is also the time when the rock reaches its maximum height.
  • #1
liz777
19
0

Homework Statement



A rock is thrown at an angle of 17 degrees above the horizontal at 28.5 m/s, from the ground.

a)How high will the rock rise above the ground?
b)What is the horizontal speed of the rock at the top of its flight?
c) How long will it take the rock to reach a vertical speed of zero m/s?


The Attempt at a Solution


First I found out what the x and y components are. x=27.25 m/s and y=8.35 m/s. Then I found the time w/ vf=vi+at. (27.25=9.8t)

a)I used the forumla d=vit+1/2at^2 and it came out to 37.87 m
=1/2(9.8)(2.78)^2
b) I'm guessing I would use the formula v=d/t. So the max height is 37.87 and the time is 2.78(1/2 the time of the rock's total air time). and I got the answer 13.62 m/s
c) I wasnt really sure on this one. Is it 2.78s, when the ball is at the top of its flight?

Any advice/help would be great. I want to make sure I'm doing this correctly. Thanks! :)
 
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  • #2


The horizontal velocity never changes
 
  • #3


This equation will be helpful
The vertical position with respect to time is given by
y(t) = y_0 + (V_0)t-4.9t^2
V_0 in the y direction is V_0sin(theta)
so 28.5sin(17)
where y'(t) = 0, the projectile has reached it's max height. Put that t into the y(t) to find the maximum height. This should also be the answer for c)
velocity in the x direction is V_0cos(theta)
so 28.5cos(17). As casedogg said, it doesn't change.
 

Related to Throwing Rocks: Analyzing Horizontal & Vertical Motion

1. What is the difference between horizontal and vertical motion?

Horizontal motion refers to the movement of an object in a straight line parallel to the ground, while vertical motion refers to the movement of an object in a straight line perpendicular to the ground.

2. How is the motion of a rock affected by air resistance?

Air resistance, also known as drag, can affect the motion of a rock by slowing it down or changing its trajectory. The amount of air resistance depends on the size and shape of the rock, as well as the density of the air.

3. What is the formula for calculating the horizontal distance traveled by a rock?

The formula for calculating the horizontal distance traveled by a rock is d = v * t, where d is the distance, v is the initial velocity, and t is the time.

4. How does the angle of release affect the motion of a rock?

The angle of release, or the angle at which the rock is thrown, can affect the motion of the rock by changing its trajectory. A higher angle of release will result in a greater vertical component of motion, while a lower angle will result in a greater horizontal component of motion.

5. How can we use the principles of horizontal and vertical motion to predict the trajectory of a thrown rock?

By understanding the principles of horizontal and vertical motion, we can use mathematical equations and calculations to predict the trajectory of a thrown rock. This involves considering factors such as the initial velocity, angle of release, and air resistance.

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