a) Let's first find the time that the projectile takes to reach its maximum height:
vy=v0y−gt,0=v0sinθ−gtt=gv0sinθ=9.8 s2m12 sm⋅sin27∘=0.55 s.Then, we can find the maximum height reached by the projectile:
ymax=v0tsinθ−0.5gt2,ymax=12 sm⋅0.55 s⋅sin27∘−0.5⋅9.8 s2m⋅(0.55 s)2=1.51 m.b) We can find the total flight time of the projectile from the formula:
tflight=2t=2⋅0.55 s=1.1 s.
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