Answer:
10 m/s
Explanation:
= Mass of arrow = 1 kg
= Mass of apple = 2 kg
= Initial Velocity of arrow = 30 m/s
= Initial Velocity of apple = 0 m/s
= Velocity of combined mass
For elastic collision
Final velocity of apple and arrow after collision is 10 m/s
Answer:
Explanation:
The distance of Earth from the Sun is and of Mars from the Sun is . Let assume that both planets have circular orbits. The centripetal accelaration can be found by using the following expression:
Since planet has translation at constant speed, this formula is applied to compute corresponding speeds:
Earth:
Mars:
Now, centripetal accelarations can be found:
Earth:
Mars:
The ratio of Earth's centripetal acceleration to Mars's centripetal acceleration is:
Answer:
the required solution is; x(t) = 0.675<em>sin</em>( 2.222t )
Explanation:
Given the data in the question;
Using both Newton's and Hooke's law;
m + k = 0, (0) = 0, (0) = 1.5
given that mass m = 9 kg
= 1.8 m
k is F / x
hence
k = F / x
given that, F = 80 N
we substitute
k = 80 / 1.8
k = 44.44
so
m + k = 0,
we input
9 + 44.44 = 0,
+ 4.9377 = 0
so auxiliary equation is,
r² + 4.9377 = 0
r² = -4.9377
r = √-4.9377
r = ±2.222i
hence, the solution will be;
x(t) = A×cos( 2.222t ) + B×sin( 2.222t )
⇒ (t) = -2.222Asin( 2.222t ) + 2.222Bcos( 2.222t )
using initial conditions
x(0) = 0
⇒ 0 = A
(t) = 1.5
1.5 = 2.222B
so
B = 1.5 / 2.222 = 0.675
Hence, the required solution is; x(t) = 0.675<em>sin</em>( 2.222t )
Answer:
u= 755 m/s
Explanation:
Lets take
Velocity of bullet = u m/s
The velocity of system after collision ,v= 5 m/s
m= 10 g = 0.01 kg
M= 1.5 kg
From linear momentum conservation( because there is no any external force on the system)
Pi= Pf
m u = ( m +m) v
0.01 x u= (1.5 + 0.01) x 5
u= 755 m/s