Question A projectile was fired from the originOof the Cartesian coordinates on the edge of a cliff with an initial velocityV0=60i+175jThe projectile rises first and then falls into the sea at pointP, as shown in the following sketch. If you know that the projectile has a time of flight of 40 seconds, that air resistance is neglected, and that the gravitational acceleration isg=10 m/s2: 1- Calculate the firing angleα. 2. Prove that the parametric equations for the projectile motion are: \[ x(t)=60 t ; y(t)=-\frac{1}{2} g t^{2}+175 t \] 3. Deduce: a- The distanceDbetween the falling pointPand the cliff. b- The heightHof the cliff from the surface of the sea.
Question A projectile was fired from the originOof the Cartesian coordinates on the edge of a cliff with an initial velocityV0=60i+175jThe projectile rises first and then falls into the sea at pointP, as shown in the following sketch. If you know that the projectile has a time of flight of 40 seconds, that air resistance is neglected, and that the gravitational acceleration isg=10 m/s2: 1- Calculate the firing angleα. 2. Prove that the parametric equations for the projectile motion are: \[ x(t)=60 t ; y(t)=-\frac{1}{2} g t^{2}+175 t \] 3. Deduce: a- The distanceDbetween the falling pointPand the cliff. b- The heightHof the cliff from the surface of the sea.
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Question A projectile was fired from the originOof the Cartesian coordinates on the edge of a cliff with an initial velocityV0=60i+175jThe projectile rises first and then falls into the sea at pointP, as shown in the following sketch. If you know that the projectile has a time of flight of 40 seconds, that air resistance is neglected, and that the gravitational acceleration isg=10 m/s2: 1- Calculate the firing angleα. 2. Prove that the parametric equations for the projectile motion are: \[ x(t)=60 t ; y(t)=-\frac{1}{2} g t^{2}+175 t \] 3. Deduce: a- The distanceDbetween the falling pointPand the cliff. b- The heightHof the cliff from the surface of the sea.
Transcribed Image Text:Question
A projectile was fired from the origin O of the Cartesian
coordinates on the edge of a cliff with an initial velocity
= 60 i+ 175 j The projectile rises first and then falls into
the sea at point P, as shown in the following sketch. If you
know that the projectile has a time of flight of 40 seconds,
that air resistance is neglected, and that the gravitational
acceleration is g = 10 m/s²:
1- Calculate the firing angle a.
2- Prove that the parametric equations for the projectile motion are:
x(t)=60t;
y(t)= gt² +175t
2
3- Deduce:
a- The distance D between the falling point P and the cliff.
b- The height H of the cliff from the surface of the sea.
H
1°
α
D→
X
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