Find Distance Traveled From 40m Height for 20m/s Velocity at 0° Angle

In summary, the conversation discusses a problem in which a ball is thrown from a height of 40 meters with a velocity of 20 m/s and an elevation angle of 0°. The goal is to determine the distance the ball will travel. Using the equations for vertical and horizontal displacement, the solution is calculated to be approximately 57 meters without factoring in air resistance.
  • #1
Gliese123
144
0

Homework Statement


From a height 40 meters up, one throw a ball with the velocity of 20 m/s. The elevation is 0°. How far does the ball come?

vo = 20 m/s
x = 40 meters
α = 0°
(g=9.82)

Homework Equations



y = v0 × t × sinα - (9.82×t2)/2

x= v0×t×cosα

The Attempt at a Solution


I put what I know in there

40 = 20×t×sin0° - (9.82×t2)/2
=>
80/9.82 = t2
=>
√(80/9.82) = t = 2.85 s (Is that right?)

Then I put all I know in the other formula to get x:
x= v0×t×cosα

x = 20×2.85×cos0°
x=57 meters
(Doesn't that feel a little too short?)

I've no answer to this question and I would be really glad if someone could confirm that this is correct calculated :)
Edit: There's no air resistance
 
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  • #2
Looks good to me.
 
  • #3
Doc Al said:
Looks good to me.

I hope so. Thanks for checkin' it :)
 

What is the formula for calculating distance traveled from initial height, velocity, and angle?

The formula for calculating distance traveled from initial height, velocity, and angle is d = h + v2sin(2θ)/g, where d is the distance traveled, h is the initial height, v is the velocity, θ is the angle (in radians), and g is the acceleration due to gravity.

Can this formula be used for any initial height, velocity, and angle?

Yes, this formula can be used for any values of initial height, velocity, and angle as long as the units are consistent and the angle is measured in radians.

How does changing the initial height affect the distance traveled?

Changing the initial height will affect the distance traveled by increasing or decreasing the value of h in the formula. The higher the initial height, the larger the value of h will be, and therefore, the greater the distance traveled will be. On the other hand, decreasing the initial height will result in a smaller value of h and a shorter distance traveled.

What happens if the velocity is increased or decreased?

Increasing or decreasing the velocity will have a direct effect on the distance traveled. The higher the velocity, the greater the distance traveled will be. This is because the value of v is squared in the formula, so even a small increase in velocity can result in a significant increase in distance traveled. Similarly, decreasing the velocity will result in a shorter distance traveled.

Can this formula be used for finding the distance traveled at angles other than 0 degrees?

Yes, this formula can be used for finding the distance traveled at any angle. However, it is important to note that the angle must be converted to radians before plugging it into the formula. Additionally, the angle must be measured from the horizontal, so a 0 degree angle would correspond to a θ value of 0 in the formula.

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