Question

A missile is fired at ground level with an initial speed of 58 m/s at an angle of 34 degrees above the horizontal. It hits a mark above the ground 2.2 seconds later.
a) what is the horizontal distance in meters from where the missile was launched to where it lands?
b)what is the vertical distance in meters from where the missile was launched to where it lands?

Answer 1

this is what i'm imagining from your description. part (a) is asking for the x measurement and part (b) is asking for the y measurement. as usual here is some solid advice: "ALWAYS draw out the problem." it helps you understand what you're getting into. second is to defer back to your notes. i'm pretty sure you went over kinematic equations. here there are anyway: \[d=v_{0}t+\frac{ 1 }{ 2 }at^2\]\[v^2=v_{0}^2+2ad\]\[v=v_{0}+at\]\[d=\frac{ t(v_{0}+v) }{ 2 }\] for part (a) I used our known values that we have which are time=2.2 s initial velocity=58 m/s and the angle at which the missile left=58 degrees. now using this we also need to separate the initial velocity into components of x and y. we need to do this because it makes it easier. We can do this by remember our trig. or SOH CAH TOA. use that on this: what we just found is the initial velocity in the x direction. repeat that process but for the y direction. now look at the kinematic equations i listed. I see we can do part (a) by using equation 1. \[d=v_{0}t+\frac{ 1 }{ 2 }at\] we have the necessary known values for this to work. now you're probably wondering about acceleration. Well in this situation there is no acceleration in the x direction. All the acceleration here is in the y direction and that's the acceleration due to gravity (-9.8 m/s^2) but since this is the x direction there is no acceleration so acceleration is just 0 here which eliminates a size able chunk from the equation. just plug and play for the rest of part (a). \[d=(58*\cos (34))*(2.2)+\frac{ 1 }{ 2 }*(0)*(2.2)^2\] and that should give you the answer to part (a). now repeat this process for part (b). look at the kinematic equations closely and select the equation that will make use of all the known values you have now and don't forget to solve for the initial velocity in the y direction by using SOH CAH TOA or another method if you see fit.