Question

If a projectile is fired with an initial velocity of V meters per second at an angle A above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations x = (V cos(A))t, y = (V sin(A))t - 1/2gt^2, where g is the acceleration due to gravity (9.8 m/s^2). (a) If a gun is fired with A = 30° and V = 500 m/s, when (in seconds) will the bullet hit the ground? Time t = 51 seconds (b) Under the conditions of (a), how far (in meters) from the gun will it hit the ground? Distance = 22084 meters (c) Under the conditions of (a), what is the maximum height (in meters) reached by the bullet? Maximum height = 5.1 meters (d) Show that the path of the bullet is parabolic by eliminating the parameter to find a Cartesian equation that describes the path. Your answer may depend on V, A, x, y, and g. If g appears in your answer, leave it in - do NOT substitute in g = 9.8 in your answer! y =

          If a projectile is fired with an initial velocity of V meters per second at an angle A
above the horizontal and air resistance is assumed to be negligible, then its position
after t seconds is given by the parametric equations
x = (V cos(A))t, y = (V sin(A))t - 1/2gt^2,
where g is the acceleration due to gravity (9.8 m/s^2).

(a) If a gun is fired with A = 30° and V = 500 m/s, when (in seconds) will the bullet
hit the ground?
Time t = 51 seconds

(b) Under the conditions of (a), how far (in meters) from the gun will it hit the ground?
Distance = 22084 meters

(c) Under the conditions of (a), what is the maximum height (in meters) reached by the
bullet?
Maximum height = 5.1 meters

(d) Show that the path of the bullet is parabolic by eliminating the parameter to find a
Cartesian equation that describes the path. Your answer may depend on V, A, x, y,
and g. If g appears in your answer, leave it in - do NOT substitute in g = 9.8 in your
answer!
y =

If a projectile is fired with an initial velocity of V meters per second at an angle A
above the horizontal and air resistance is assumed to be negligible, then its position
after t seconds is given by the parametric equations
x = (V cos(A))t, y = (V sin(A))t - 1/2gt^2,
where g is the acceleration due to gravity (9.8 m/s^2).

(a) If a gun is fired with A = 30° and V = 500 m/s, when (in seconds) will the bullet
hit the ground?
Time t = 51 seconds

(b) Under the conditions of (a), how far (in meters) from the gun will it hit the ground?
Distance = 22084 meters

(c) Under the conditions of (a), what is the maximum height (in meters) reached by the
bullet?
Maximum height = 5.1 meters

(d) Show that the path of the bullet is parabolic by eliminating the parameter to find a
Cartesian equation that describes the path. Your answer may depend on V, A, x, y,
and g. If g appears in your answer, leave it in - do NOT substitute in g = 9.8 in your
answer!
y =

Added by Diane C.

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