A) A particle withintial velocity -3i+5j , undergoesaconstant acceleration a=3m/

Question

A) A particle withintial velocity -3i+5j, undergoesaconstant acceleration a=3m/s2at an angle of =220ofrom the psitive direction of the x axis. i) What is the particle's velocityat t=5s ii) How long does it take to reachthe maximum height? iii) Find the horizontaldisplacement of the particle when it reachs the maximum. --------------------------------------------------------------------------------------------------------- B) A parachutistbails out and freely falls 50m. Then theparachute opens, and thereafter she decelerates at2m/s2. She reaches the groundwith a speed of 3.0m/s. i) How long is the parachutist inthe air? ii) At what height does the fallbegain? --------------------------------------------------------------------------------------------------------- A) A particle withintial velocity -3i+5j, undergoesaconstant acceleration a=3m/s2at an angle of =220ofrom the psitive direction of the x axis. i) What is the particle's velocityat t=5s ii) How long does it take to reachthe maximum height? iii) Find the horizontaldisplacement of the particle when it reachs the maximum. --------------------------------------------------------------------------------------------------------- B) A parachutistbails out and freely falls 50m. Then theparachute opens, and thereafter she decelerates at2m/s2. She reaches the groundwith a speed of 3.0m/s. i) How long is the parachutist inthe air? ii) At what height does the fallbegain? ---------------------------------------------------------------------------------------------------------

Explanation / Answer

initial velocity v0 =-3 i + 5 j, a = 3m/s2 , =220o, a = 3cosi + 3sinj,
i) What is the particle's velocity att = 5s
v(t)= v0+ at = -3i + 5j + (3cosi + 3sinj)*5 = (15cos - 3) i+ (15sin + 5) j =(-14.5 i - 4.64 j)m/s
ii) How long does it take to reachthe maximum height?
vy(t) = 0, (v0 +at)y = 0
-3i + 5j + (3cos i+ 3sin j)*t = 0
5 + 3sin*t = 0
t = 2.59 s
iii) Find the horizontal displacement ofthe particle when it reaches the maximum.
v(t) =v0 + at
r(t) = v0t + at2/2= (-3 i + 5 j)t + (3cosi + 3sinj)t2/2
x(2.59) = -3*2.59 + 3cos(220)*2.592/2 = -15.5m

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