Help Physics Question: An athlete executing a long jump leaves the ground at a 25° angle and travels 7.30 m.?

Question

(a) What was the takeoff speed? .... m/s
(b) If this speed were increased by just 6.0%, how much longer would the jump be? .... m

and also, this question : 2). A hunter aims directly at a target (on the same level) 120 m away.

(a) If the bullet leaves the gun at a speed of 200 m/s, by how much will it miss the target?
(b) At what angle should the gun be aimed so as to hit the target?



Please help me to do this problem and also please include the work. Thank you soo much for helping me to do this.. Thank You :)

Answer 1

For the jumper
the displacement is
7.3=Cos(25)*v*t
where v is the speed at take-off and t is the flight time
We also know that
sin(25)*v*t-.5*g*t^2=0
since there are two roots, one is t=0, the take-off, and the second is
t=2*sin(25)*v/g

plugging into the displacement equation
7.3=2*Cos(25)*v^2*sin(25)/g

solve for v, then for t

if v'=1.06*v
t'=2*1.06*sin(25)*v/g

the new length is
d'=1.06*cos(25)*t'

2. The flight time to target is
120=200*t
so t=3/5 seconds
the drop is
.5*g*t^2
using g=10
18/15 or over 1 meter

to hit the target, the angle is th
flight time to the target is
120=200*cos(th)*t
and the drop is 0, so
0=sin(th)*200*t-.5*g*t^2
solve for the root greater than 0
t=sin(th)*400/2
and plug into the time to target to solve for th

120=200*cos(th)*sin(th)*200

120/(200^2)=sin(th)*cos(th)

0.003=sin(th)*cos(th)
th=0.172 degrees

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Answer 2

assume 5.80m is horizontal there's a style formula you ought to use yet instructors in many cases do no longer choose you to apply it, so i will supply it an end. shall we are saying time taken is t vx = 5.eighty/t delta y = 0 so 0 = viyt + a million/2 g t^2 or t = 2viy/9.8 so vx = 5.8*9.8/(2viy) or vxviy = 5.8*9.8/2 = vcos20vsin20 clean up v^2 = 5.8*9.8/(2*cos20*sin20) for v The formula is variety = v^2sin(2theta)/g increasing v by ability of 5% ability variety will strengthen by ability of 10% So 5.eighty + .580 to coach it, upload 5% to v chanced on before and locate new variety