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Height and Range in physics?
On a distant planet, golf is just as popular as it is on earth. A golfer tees off and drives the ball 1.7 times as far as he would have on earth, given the same velocities on both planets. The ball is launched at a speed of 40 m/s at an angle of 46° above the horizontal. When the ball lands, it is at the same level as the tee.
(a) On the distant planet, what is the maximum height of the ball?
m
(b) On the distant planet, what is the range of the ball?
i keep gettin 674 for the first one and its not right and i cant figure out what i’m gettin wrong so i havent even attempted the second part, i’d appreciate any help
In general,
Vv= V sin(46)
Vh= V cos(46)
And assuming no air resistance
t(up)= Vv/g
t(down)= t(up)
t(total)=2 t(up)= 2Vv/g
the horizontal distance traveled is then
S= Vh t(total)
S= Vh [2 Vv/g]
S= 2Vh V sin(46)/g
S= 2Vcos(46) V sin(46)/g
S= V^2 sin(2 x 46)/g
a) h= 0.5gt^2 (let’s do part b first)
from part b
t(total)= 9.97 then t(up)= 4.99 sec
g=5.77m/s^2
h= 0.5 (5.77) (4.99)^2=71.8 m (72 m )
b) Let’s compute for Earth first
S1= 2Vh V sin(46)/g
on the other planet it would be
S2= 1.7 S1=1.7 x 2 Vcos(46) V sin(46)/g since 2 sin(A) cos(A)= sin(2A)
S2= 1.7 S1=1.7 x V^2 sin(2x 46)/g
S2= 1.7 x (40)^2 sin(2x 46)/9.8
S2=277 m
t= S2/Vh= S2/ V cos(46)
t= 277 / (40 cos(46))=
t= 9.97 this is total time
Now we have to find g
S= V^2 sin(2×46)/g
g= V^2 sin(2×46)/S
g=(40)^2 sin(92)/ 277= 5.77 m/s^2
now we can go back to part a)
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