Calculate the velocity of the projectile

In summary, a stone is thrown with an initial velocity of 100 m/s and the task is to calculate its velocity at a height of 10 m. The solution involves using the equations for resultant velocity and the components of velocity in the x and y directions, taking into account the acceleration of gravity and neglecting the effect of air molecules. The error in the given solution is with the equation for Vy, which should be squared and rearranged to be dimensionally correct.
  • #1
Fadi A.Saif
6
0

Homework Statement


A stone was thrown with initial velocity of 100 m/s. Calculate the velocity of the projectile at 10 m of height. (Consider g=10m/s^2, and neglect the effect of air molecules)


Homework Equations



where's the error in the following sollution?


The Attempt at a Solution


Vr= sqrt((Vx)^2+(Vy)^2)...(1) (Resultant velocity).
Vx= Vi cos(a)...(2)
Vy=Vi sin(a)+(-2gy)...(3)
sub. (2)& (3) in (1)
Vr = sqrt(Vi^2 (cos(a))^2+Vi^2 (sin(a))^2+(-2gy)); taking Vi as a common factor, and sqrt of both sides; we get
Vr = sqrt(Vi^2-2gy) then we proceed by applying the given data from the problem
 
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  • #2


The error is right here

Vy=Vi sin(a)+(-2gy)

This equation is not dimensionally correct.
 
  • #3


Thanks Kuruman... so I believe it should be like this
Vy^2= Vi^2 (sin(a))^2 - 2gy.
 
  • #4


That's more like it.
 

FAQ: Calculate the velocity of the projectile

What is the formula for calculating the velocity of a projectile?

The formula for calculating the velocity of a projectile is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.

How do I find the initial velocity of a projectile?

To find the initial velocity of a projectile, you can use the formula v = u + at and solve for u. Alternatively, if you have the distance and time of the projectile's motion, you can use the formula u = d/t, where d is the distance and t is the time.

Can I calculate the velocity of a projectile without knowing its acceleration?

Yes, you can calculate the velocity of a projectile without knowing its acceleration if you have the distance and time of the projectile's motion. Use the formula u = d/t, where d is the distance and t is the time. However, if the projectile's acceleration is not constant, this method will not provide an accurate result.

How does air resistance affect the velocity of a projectile?

Air resistance can decrease the velocity of a projectile as it travels through the air. This is due to the force of air resistance acting in the opposite direction of the projectile's motion. The greater the air resistance, the more it will slow down the projectile's velocity.

What units should be used when calculating the velocity of a projectile?

The units used for velocity are typically meters per second (m/s) or feet per second (ft/s). However, depending on the measurement units used for distance and time, the resulting velocity may need to be converted to a different unit. It is important to use consistent units when calculating velocity.

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