
急!!!!!高数题,,不大会做,求救高手帮忙解答!!!
Aprojectileisfiredfromacannon.Assumethatairre-sistanceisnegligible,sotheonlyforceacti...
A projectile is fired from a cannon. Assume that air re-
sistance is negligible, so the only force acting on the projectile is gravity. Recall
Newton's Second law: force = mass times acceleration:
F = ma :
We set up the axes so that the projectile starts at the origin. Since gravity acts
downward, we have that
a = - gj
where g ≈9.8m/s2.
(a) Find a formula for the velocity v(t) of the projectile at time t, knowing that
the initial velocity is v0.
(b) Find a formula for the position r(t) of the projectile at time t, knowing that
the initial position of the projectile is the origin: r(t) = 0.
(c) Suppose the cannon is aimed upward at an angle of and the initial speed of
the projectile is s.
Show that the parametric equations of the trajectory of the projectile are:
x(t) = (s cos α阿尔法)t, y(t) = (s sin α)t - (gt^2)/2
(d) The particle is at the ground when y(t) = 0. Obviously this happens at the
beginning, t = 0. What is the other time t when this occurs?
(e) Suppose α (阿尔法)= 45° and the initial speed is s = 150m=s2. Where does the
projectile hit the ground?
(c)那个angle是阿尔法,没打出来 展开
sistance is negligible, so the only force acting on the projectile is gravity. Recall
Newton's Second law: force = mass times acceleration:
F = ma :
We set up the axes so that the projectile starts at the origin. Since gravity acts
downward, we have that
a = - gj
where g ≈9.8m/s2.
(a) Find a formula for the velocity v(t) of the projectile at time t, knowing that
the initial velocity is v0.
(b) Find a formula for the position r(t) of the projectile at time t, knowing that
the initial position of the projectile is the origin: r(t) = 0.
(c) Suppose the cannon is aimed upward at an angle of and the initial speed of
the projectile is s.
Show that the parametric equations of the trajectory of the projectile are:
x(t) = (s cos α阿尔法)t, y(t) = (s sin α)t - (gt^2)/2
(d) The particle is at the ground when y(t) = 0. Obviously this happens at the
beginning, t = 0. What is the other time t when this occurs?
(e) Suppose α (阿尔法)= 45° and the initial speed is s = 150m=s2. Where does the
projectile hit the ground?
(c)那个angle是阿尔法,没打出来 展开
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