Answer:
2.908 s
Step-by-step explanation:
The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.
For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...
h(t) = -16t² +v₀t +s₀
where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.
0 = -16t² +65sin(44°) +4
Dividing by -16 gives ...
0 = t^2 -2.82205t -0.2500
Using the quadratic formula, we find ...
t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099
t ≈ 2.90802
It will take about 2.908 seconds for the discus to reach the ground.
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Comment on the question
You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.
