physics

posted by .

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected into a liquid so that it initially has a horizontal velocity of u in the +x direction as shown. The initial speed in the vertical direction (y) is zero. The gravitational acceleration is g. Consider the cartesian coordinate system shown in the figure (+x to the right and +y downwards).

Express the answer of the following questions in terms of some or all of the variables C1, r, m, g, vx, vy, u and t (enter C_1 for C1, v_x for vx and v_y for vy). Enter e^(-z) for exp(-z) (the exponential function of argument -z).

(a) What is component of the acceleration in the x direction as a function of the component of the velocity in the x direction vx? express your answer in terms of vx, C1, r, g, m and u as needed:

ax=

(−1mC1⋅r)⋅vx
(b) What is the acceleration in the y direction as a function of the component of the velocity in the y direction vy? express your answer in terms of vy, C1, r, g, m and u as needed:

ay=

(c) Using your result from part (a), find an expression for the horizontal component of the ball's velocity as a function of time t? express your answer in terms of C1, r, g, m, u and t as needed: (enter e^(-z) for exp(-z)).

vx(t)=

u⋅e−tmC1⋅r
(d) Using your result from part (b), find an expression for the vertical component of the ball's velocity as a function of time t? express your answer in terms of C1, r, g, m, u and t as needed: (enter e^(-z) for exp(-z)).

vy(t)=

(e) How long does it take for the vertical speed to reach 99% of its maximum value? express your answer in terms of C−1, r, g, m and u as needed:

t=

(f) What value does the horizontal component of the ball's velocity approach as t becomes infinitely large? express your answer in terms of C1, r, g, m and u as needed:

(g) What value does the vertical component of the ball's velocity approach as t becomes infinitely large? express your answer in terms of C1, r, g, m and u as needed

• physics -

ax=(-C_1*r*v_x)/m

• physics -

a)(-C_1*r*v_x)/m
b)g-(C_1*r*v_y)/m
c)u*e^(-(C_1*r*t)/m)
d)((m*g)/(C_1*r))-((m*g)/(C_1*r))*e^(-(C_1*r*t)/m)
e)4.6*(m/(C_1*r))
f)0
g)(m*g)/(C_1*r)

Similar Questions

1. mitx 8.01x Classical Mechanics

For the following 3 vectors A⃗ =2y^+3z^ B⃗ = 3 x^+2z^ C⃗ = 3 x^+3y^ Calculate the following: (a) A⃗ ⋅(B⃗ +C⃗ )= (b) D⃗ =A⃗ ×(B⃗ +C⃗ ) Dx= Dy= Dz= (c) A⃗ ⋅(B⃗ …
2. physics

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
3. Physisc(help)

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
4. physics

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
5. physics

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
6. physics

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
7. physics

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
8. PHYSICS(HELP)

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
9. PHYSICS(PLS HELP)

At low speeds (especially in liquids rather than gases), the drag force is proportional to the speed rather than it's square, i.e., F⃗ = −C1rv⃗ , where C1 is a constant. At time t = 0, a small ball of mass m is projected …
10. phy

Given three vectors a⃗ =−i⃗ −4j⃗ +2k⃗ , b⃗ =3i⃗ +2j⃗ −2k⃗ , c⃗ =2i⃗ −3j⃗ +k⃗ , calculate a⃗ ⋅(b⃗ ×c⃗ )

More Similar Questions