Initial vertical component of velocity is 61 m/s

[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

 

[chroot]

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

 

[M98Ranger]

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.