Answer to Question #160973 in Mechanics | Relativity for jireh

Question #160973

aa projectile is launched at initial velocity of 12m/s and angle of 27 degree. (a) what is the maximum height reached by the projectile? (b) what is the time taken by the projectile? show your solution.


1
Expert's answer
2021-02-03T16:11:51-0500

a) Let's first find the time that the projectile takes to reach its maximum height:


vy=v0ygt,v_y=v_{0y}-gt,0=v0sinθgt0=v_0sin\theta-gtt=v0sinθg=12 mssin279.8 ms2=0.55 s.t=\dfrac{v_0sin\theta}{g}=\dfrac{12\ \dfrac{m}{s}\cdot sin27^{\circ}}{9.8\ \dfrac{m}{s^2}}=0.55\ s.

Then, we can find the maximum height reached by the projectile:


ymax=v0tsinθ0.5gt2,y_{max}=v_0tsin\theta-0.5gt^2,ymax=12 ms0.55 ssin270.59.8 ms2(0.55 s)2=1.51 m.y_{max}=12\ \dfrac{m}{s}\cdot0.55\ s\cdot sin27^{\circ}-0.5\cdot9.8\ \dfrac{m}{s^2}\cdot(0.55\ s)^2=1.51\ m.

b) We can find the total flight time of the projectile from the formula:


tflight=2t=20.55 s=1.1 s.t_{flight}=2t=2\cdot0.55\ s=1.1\ s.

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