How to Find initial Velocity at 90 degrees with only a time variable given

[cloakblade5]

I am given the information that a nerf dart is launched upwards at a 90 degrees with the top of the launcher at 1.953ft and that it hits the ground .43 seconds later. I am then tasked with finding the initial velocity of the launcher and I have no idea where to start.

 

[Hootenanny]

I am given the information that a nerf dart is launched upwards at a 90 degrees with the top of the launcher at 1.953ft and that it hits the ground .43 seconds later. I am then tasked with finding the initial velocity of the launcher and I have no idea where to start.

Welcome to PF cloakblade5,

You must have some idea as where to start, which concept(s) are involved? What are the relevant equations?

Please be aware the according to our forum guidelines, you are required to post an attempted solution when asking for homework assistance.

 

[baba89]

To find the initial velocity in this scenario, we can use the equation: v = u + at, where v is the final velocity (which in this case is 0 since the dart hits the ground), u is the initial velocity, a is the acceleration due to gravity (9.8 m/s^2), and t is the time (0.43 seconds).

First, we need to convert the given distance and time into SI units (meters and seconds). 1.953ft is approximately 0.595 meters. Plugging in the values into the equation, we get: 0 = u + (9.8 m/s^2)(0.43 s).

Solving for u, we get u = -4.214 m/s. However, this value is negative because our initial velocity is directed upwards, opposite to the direction of gravity. Therefore, the initial velocity of the nerf dart launcher at 90 degrees is approximately 4.214 m/s.

To double check our answer, we can also use the equation: s = ut + 1/2at^2, where s is the displacement (0.595 meters), u is the initial velocity (which we just solved for), a is the acceleration due to gravity, and t is the time (0.43 seconds).

Plugging in the values, we get: 0.595 = (4.214 m/s)(0.43 s) + 1/2 (9.8 m/s^2)(0.43 s)^2. Solving for u, we get the same result of approximately 4.214 m/s.

Therefore, the initial velocity of the nerf dart launcher at 90 degrees is 4.214 m/s.