A dart is thrown upwards with an initial velocity of 64 ft./s at an angle of elevation of 52° consider the position T with no air resistance, find the parametric equation that models a solution as well as find all possible values of X that represent the solution
Accepted Solution
A:
Solution
Using the equation of motion and finding the horizontal displacement
$$u=64c0s\left(52\right)$$
a=0
$$x\left(t\right)=64c0s\left(52\right)t+\frac{1}{2}\left(0\right)t^2$$
$$x\left(t\right)=64c0s\left(52\right)t$$
Since acceleration due to gravity acts on the dart in a vertically downward direction
a=-32 ft/s
u=64sin(52)
$$y\left(t\right)=64sin\left(52\right)t+\frac{1}{2}\left(-32\right)t^2$$
$$y\left(t\right)=64sin\left(52\right)t-16t^2$$