## anonymous one year ago A ball is to be shot from level ground with a certain speed. The figure shows the range R it will have versus the launch angle θ0. The value of θ0 determines the flight time; let tmax represent the maximum flight time. What is the least speed the ball will have during its flight if θ0 is chosen such that the flight time is 0.320tmax?

1. IrishBoy123

" The figure shows the range R it will have versus the launch angle θ0." which figure?

2. anonymous

|dw:1433232959111:dw|

3. anonymous

the highest peak is at 240 :)

4. anonymous

5. anonymous

is my answer correct 41.05 m/s?

6. anonymous

or is it 45.13 m/s

7. IrishBoy123

1) how can you answer this without having a launch speed? 2) i am somewhat concerned that this question is misleading. indulge me for a second. for a fixed launch speed, v, the flight time is $$2 \times \frac{v sin \theta}{g} = 2\frac{v sin \theta}{g}$$, right? that's up and back down again. now, to find the max flight time, $$\frac{dt }{d \theta} = 2\frac{v cos \theta}{g} = 0$$, giving $$\theta = \pi/2$$. whcih makes sense: if the launch speed is fixed, you maximise flight time by throwing it straight up in the air. are you doing it this way or are you assuming that max range coincides with max flight time - because it doesn't. max range occurs at $$\theta = \pi/4$$ but that is not the max flight time possible for a fixed launch velocity.