Initial vertical component of velocity is 61 m/s

In summary, the toy is thrown up with an initial vertical velocity of 61 m/s and an initial horizontal velocity of 10 m/s. After two seconds, the toy's vertical velocity decreases to 41.4 m/s due to the effect of gravity, while its horizontal velocity remains constant at 10 m/s. To find the total speed, you can represent the velocities with arrows and add them together.
  • #1
espo
a toy is thrown up; its initial vertical component of velocity is 61 m/s and its initial horizontal component of velocity is 10m/s what is the toys speed two seconds later; please help
 
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  • #2
Hi espo,

Your teacher gave you the velocity in components to make the calculation easier for you to do. The velocity in the horizontal direction is independent of its velocity in the vertical direction.

As you know, gravity affects the toy in the vertical direction. Gravity makes the toy accelerate downwards at 9.8 m/s.

As you have indicated you understand, the toy's vertical velocity is decreasing (i.e. becoming more downwards) by 9.8 m/s every second it is in flight. Two second later, the toy's vertical velocity is 61 - 2*9.8 = 41.4 m/s. You can see that it is still moving upward, but less quickly than it was initially.

What about the horizontal component? You may be surprised to learn that it is not affected at all by gravity. The toy moves with a constant 10 m/s of horizontal velocity at all times (until it hits the ground, of course).

So now you just need to find the total speed when the toy is moving sideways at 10 m/s and upwards at 41.4 m/s. You can represent those velocities with arrows, and add the arrows, just as I showed you here:

https://www.physicsforums.com/showthread.php?s=&postid=87756#post87756

What do you get for the total velocity?

- Warren
 
  • #3


To answer this question, we need to use the formula for velocity: V = V0 + at, where V is the final velocity, V0 is the initial velocity, a is the acceleration, and t is the time.

In this scenario, the toy's initial vertical velocity (V0) is 61 m/s and its initial horizontal velocity is 10 m/s. Since the toy is being thrown up, we can assume that the acceleration is due to gravity, which is -9.8 m/s^2.

Plugging in the values, we get:
V = 61 m/s + (-9.8 m/s^2) * 2 s
V = 61 m/s - 19.6 m/s
V = 41.4 m/s

Therefore, the toy's speed two seconds later is 41.4 m/s. It is important to note that this is the total velocity, taking into account both the vertical and horizontal components. If we want to find the speed in just the vertical direction, we can use the Pythagorean theorem to calculate the magnitude of the velocity:
V = √(41.4 m/s)^2 + (10 m/s)^2
V = √(1706.96 m^2/s^2)
V = 41.3 m/s

I hope this helps! Let me know if you have any further questions.
 

1. What does "initial vertical component of velocity is 61 m/s" mean?

This means that at the beginning of motion, the object has a vertical velocity of 61 m/s. This velocity is directed upwards or downwards, depending on the direction of the motion.

2. How is the initial vertical component of velocity calculated?

The initial vertical component of velocity can be calculated by dividing the initial vertical velocity by the time taken for the object to reach that velocity. This can be represented as: vy0 = Δy/Δt.

3. Is the initial vertical component of velocity the same as the initial velocity?

No, the initial vertical component of velocity only represents the vertical component of the initial velocity. The initial velocity is the total velocity of the object, which includes both the vertical and horizontal components.

4. How does the initial vertical component of velocity affect the object's motion?

The initial vertical component of velocity determines the initial direction and speed of the object's vertical motion. It affects the object's acceleration and determines whether the object will move upwards or downwards.

5. Can the initial vertical component of velocity change during motion?

Yes, the initial vertical component of velocity can change during motion due to external forces such as gravity or air resistance. It can also be changed by the object's own movement, such as when it changes direction or speed.

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