Solving Ten-Pin Bowling Physics with Proportional Signs

[moobs93]

i know this is really simple, but I'm not very good at working with proportional signs..

a novice ten-pin bowler, slightly "lofts" the ball (releases it too late and lifts it into the air so that it crashes to the ground. If the ball was released with a velocity of 3.5 m/s at an angle of 15 degrees above the horizontal, calculate:

a) the x and y components
b) the maximum height achieved by the ball
c) the time flight of the ball
d) how far down the lane the ball lands, measured from the release point
e) all of the above again, if the ball was 20% heavier

so i got the (a)-(d) taking the original mass as m. and started (e) by assuming the second mass would be (m+0.2m) and that the force applied by the bowler on the ball, would remain constant so the acceleration would change in proportion to the mass change of an additional 20%

my first question is; how do you represent the decrease in acceleration mathematically?
using F=ma, where m is now m(1+0.2)
my belly-flop attempt:
F=ma
a=K/m (where K is the constant force)
so mass is inversely proportional to the acceleration
does that mean the new acceleration is a(1-0.2) or am i completely off it?

and my second question is, how do you calculate the new initial velocity from the new acceleration? or rather, how do you calculate the time it takes to reach the maximum height (highest vertical displacement) using the new value for accleration? which i can then use to solve for the new initial velocity

once i have that i can finish the question myself
thanks heaps

 

[Redbelly98]

i know this is really simple, but I'm not very good at working with proportional signs..

a novice ten-pin bowler, slightly "lofts" the ball (releases it too late and lifts it into the air so that it crashes to the ground. If the ball was released with a velocity of 3.5 m/s at an angle of 15 degrees above the horizontal, calculate:

a) the x and y components
b) the maximum height achieved by the ball
c) the time flight of the ball
d) how far down the lane the ball lands, measured from the release point
e) all of the above again, if the ball was 20% heavier

so i got the (a)-(d) taking the original mass as m. and started (e) by assuming the second mass would be (m+0.2m) and that the force applied by the bowler on the ball, would remain constant so the acceleration would change in proportion to the mass change of an additional 20%

my first question is; how do you represent the decrease in acceleration mathematically?
using F=ma, where m is now m(1+0.2)
my belly-flop attempt:
F=ma
a=K/m (where K is the constant force)
so mass is inversely proportional to the acceleration
does that mean the new acceleration is a(1-0.2) or am i completely off it?

and my second question is, how do you calculate the new initial velocity from the new acceleration? or rather, how do you calculate the time it takes to reach the maximum height (highest vertical displacement) using the new value for accleration? which i can then use to solve for the new initial velocity

once i have that i can finish the question myself
thanks heaps

Welcome to physics forums.

I interpret the question to mean the same given initial conditions apply (3.5 m/s at 15° to the horizontal), and the ball is 20% heavier.