We can still resolve an initial velocity into v_x and v_y, even if our angle of

ID: 1537383 • Letter: W

Question

We can still resolve an initial velocity into v_x and v_y, even if our angle of launch is negative. What affect does a downward firing angle have on flight time? Why do you suppose this is? What formula can we use that supports your explanation? How does this negative angle affect maximum range? Why do you suppose this is? What formula can we use that supports your explanation? Back to our pirates. A small dingy is floating up to a pirate's ship full of would be boarders. He angles his cannon downward at -15 degree while 3.0 m above the water. He fires his cannon at 95 m/s. The small boat of unfortunate crewmen is 20 m away. Do they survive their foolhardy errand?

Explanation / Answer

part a:

downward firing angle reduces flight time.

part b:

when the projectile is launched with upward firing angle, the projectile rises to a maximum height , then comes to original height

and then falls down.

the time taken to reach the maximum height and then come back to original height is eliminitated in case of downward firing angle

so flight time is less.

part c:

displacement=initial velocity*time+0.5*acceleation*time^2

for downward launch, initial velocity and acceleration have same sign

and hence value for time is less.

part d:

maximum range is reduced.

part e:

maximum range is initial horizontal velocity*flight time

but as flight time reduces, maximum range reduces

part f:

maximum range is initial horizontal velocity*flight time

part g:

initial vertical speed=95*sin(15)=24.588 m/s

distance to water=3 m

acceleration=9.8 m/s^2

if time taken is t seconds,

then 3=24.588*t+0.5*9.8*t^2

==>4.9*t^2+24.588*t-3=0

t=0.11918 seconds

horizontal speed=95*cos(15)=91.763 m/s

distance travelled by this time=91.763*0.11918=10.936 m

yes, the boarders will survive as they are 20 m away

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We can still resolve an initial velocity into v_x and v_y, even if our angle of

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