Projectile Motion Doubt
I'm having a hard time to visualize the second part. On one hand, the range of the projectile should be maximized/increased, but also on the other hand, time of flight must be minimized/decreased. So, how to figure out what to do?
41 Replies
@Gyro Gearloose
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.OB is y axis ? Or z and have they given that the stones velocity changes when it comes to contact with water
We don't need its velocity when it comes in contact with water no? (Assuming that river is thin)
Also, yeah OB is y-axis.
Same width as the block?
Ok
Yeah, basically no interaction with water is needed. The projectile must hit the block directly.
V1 is 2 and v2 is 10?
Yep.
i get the idea of maximising range but how is the idea of decreasing the time of flight coming
My thought was: Imagine the block moving ahead for some time t, now the projectile must either reach the block far away or can meet it at a nearer place where time of flight is less.
if Z component is fixed you cant change the time of flight no ?
of the projectile
it will always be 4 seconds
But z component is not fixed.
Only the net velocity is fixed.
uh
ok then i will go try it again
@SirLancelotDuLac answer is 12.23?
v1= 2 , v2= 20 ??
V2 is 10 V1 is correct
for b part what i was able to think was Vx=2 must stay fixed to cover the distance travelled by boat in x dirn
Vz and Vy can be varied
time of flight = t = 2Vz/10
distance covered in y = 40 = fixed = Vyt this gives VyVz = 200
since the speed is same : 2^2 + 20^2 + 20^2 = Vx^2+ Vy^2 + Vz^2
=> 20^2+ 20^2 = Vy^2 + Vz^2
we can solve these relations to get soln
why is V2 10
t=Vz/10 is wrong ??
oh got it
It's 2vz/10
yeah
Vx is not necessarily 2 the stone is thrown after some time so it doesn't have to be the same speed
It should be greater than 2 or else it can't catch up
aise toh we can get infinite time
See the second case
not mentioned that its thrown after some lag
No there are some constraints speed is fixed net speed can only be ✓504
What else do you think what is the maximum value of time t at which it is possible to throw the stone to hit the block is
aise toh wait very long , keep Vz=0 and supply all velocity in x and y dirn
Try it out see if you get ans more than 12.23
how are u getting 12.23
Maximum range is 50.4 and it has to travel 40m in y dirn so 30.67m in x dirn and maximum range will be when angle is 45 degrees
By this you get it
I used calculator
It's given as 12.18. Can you share your solution tho?
@SirLancelotDuLac by 'keeping speed fixed' does it mean the speed we get in part 1?
Yep. (Magnitude-wise)
Why am I blanking on how to get v2 for part 1?
Oh nvm
,rotate
Yeah, but the same question: How do we know the "extremal case" is the one where range is maximum?
when range is maxium the distance traveled by the block will also be maximum so the total time the block travels will be maximum
Ah, so basically we have to maximize the total time travelled by the block?
yes
Thanks.
+solved @hithav
Post locked and archived successfully!
Archived by
<@1075951732460376214> (1075951732460376214)
Time
<t:1742562402:R>
Solved by
<@726641475080683522> (726641475080683522)