 #1
 Homework Statement:
 Hello. Recently in my class we started Projectile motion but I seem to have some trouble. Can you help me with these questions?
 Relevant Equations:

v=u+at
vSinθ
vCosθ
S=ut
v=ut+1/2at²
V²=U² + 2as
1)Find the range of the gun when the muzzle speed is 400m/s and the elevation 24.5°
 I tried to find " Time " via t= [vu]/a by substituting it through cos>
t= ( 0 [400cos24.5] )/10 and got [ 36.39 ].
Which I then substituted in S=ut> S= ( 400cos24.5 ) x 36.39=13245.3.
[ the answer in the answer key is 10.9 km ]
2)A target is 10 km from a gun and the gun's muzzle speed is 400 m/s. What angle of projection. What angle of projection will ensure a hit?
 I used cos1 (10000/400 ) and got cos1(25). I think its wrong.
So I tried θ = 400sin24.5=165.877
[ the answer in the answer key is 71° 5' ; 18° 55' ]
3)A projectile has a muzzle speed of 70 m/s. what is the range on a horizontal plane if the angle of projection is 15° . Find the error, at this range if the error in the elevation is 0.25°
 I used t = v  u/ a and substituted the values in T= ( 0  70sin15 ) / 10=1.81
And using formula S=ut, I multiplied it>S= ( 70cos15 ) x 1.81=122.5 m
[ the answer in the answer key is 250m ; ± .7.6 m ]

PS: Can you tell me, when do you use cos and sin in questions like these?
do you use sin when something goes up or is in the air? And cos for horizontal range of a projectile/object?
If you can help,it would be much appreciated
 I tried to find " Time " via t= [vu]/a by substituting it through cos>
t= ( 0 [400cos24.5] )/10 and got [ 36.39 ].
Which I then substituted in S=ut> S= ( 400cos24.5 ) x 36.39=13245.3.
[ the answer in the answer key is 10.9 km ]
2)A target is 10 km from a gun and the gun's muzzle speed is 400 m/s. What angle of projection. What angle of projection will ensure a hit?
 I used cos1 (10000/400 ) and got cos1(25). I think its wrong.
So I tried θ = 400sin24.5=165.877
[ the answer in the answer key is 71° 5' ; 18° 55' ]
3)A projectile has a muzzle speed of 70 m/s. what is the range on a horizontal plane if the angle of projection is 15° . Find the error, at this range if the error in the elevation is 0.25°
 I used t = v  u/ a and substituted the values in T= ( 0  70sin15 ) / 10=1.81
And using formula S=ut, I multiplied it>S= ( 70cos15 ) x 1.81=122.5 m
[ the answer in the answer key is 250m ; ± .7.6 m ]

PS: Can you tell me, when do you use cos and sin in questions like these?
do you use sin when something goes up or is in the air? And cos for horizontal range of a projectile/object?
If you can help,it would be much appreciated
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