A girl of a mass 50 kg jumps with a horizontal velocity of 10m/s onto a stationary cart with frictionless wheels . The mass of the cart is 5 kg . What is her velocity as the cart starts moving? Assuming that there is no external unbalanced force working in horizontal direction?
Answers
Answer:
Given : M
girl
=40 kg u
girl
=5 m/s M
cart
=3 kg
Initial velocity of cart u
cart
=0
Let the final velocity of cart be V.
Applying conservation of linear momentum : P
i
=P
f
Or M
girl
u
girl
+M
cart
u
cart
=(M
girl
+M
cart
)V
Or 40×5+3×0=(40+3)V
⟹ V=
43
200
m/s
Answer:
ʟᴇᴛ ᴠ ʙᴇ ᴛʜᴇ ᴠᴇʟᴏᴄɪᴛʏ ᴏғ ᴛʜᴇ ɢɪʀʟ ᴏɴ ᴛʜᴇ ᴄᴀʀᴛ ᴀs ᴛʜᴇ ᴄᴀʀᴛ sᴛᴀʀᴛs ᴍᴏᴠɪɴɢ.
ᴛʜᴇ ᴛᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴀ ᴏғ ᴛʜᴇ ɢɪʀʟ ᴀɴᴅ ᴄᴀʀᴛ ʙᴇғᴏʀᴇ ᴛʜᴇ ɪɴᴛᴇʀᴀᴄᴛɪᴏɴ = (50 x 5 ᴍ s-1) + (4 x 0 ᴍ s-1)
= 250 ᴋɢ ᴍ s-1
ᴛʜᴇ ᴛᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴀ ᴀғᴛᴇʀ ᴛʜᴇ ɪɴᴛᴇʀᴀᴄᴛɪᴏɴ = (50 + 4) ᴋɢ x ᴠ ᴍ s-1
= 54 ᴠ ᴋɢ ᴍ s-1
ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ʟᴀᴡ ᴏғ ᴄᴏɴsᴇʀᴠᴀᴛɪᴏɴ ᴏғ ᴍᴏᴍᴇɴᴛᴜᴍ,
ᴛᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ʙᴇғᴏʀᴇ ᴛʜᴇ ɪɴᴛᴇʀᴀᴄᴛɪᴏɴ = ᴛᴏᴛᴀʟ ᴍᴏᴍᴇɴᴛᴜᴍ ᴀғᴛᴇʀ ᴛʜᴇ ɪɴᴛᴇʀᴀᴄᴛɪᴏɴ
→ 54 ᴠ = 250
ᴠ = 4.36 ᴍ/s